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دسترسی آزاد مقاله
1 - حل دستگاه نامتناهی معادلات انتگرال غیرخطی بوسیله عملگر تراکمی - تعمیمیافته مر - کلر، اندازه نافشردگی و روش هموتوپی اختلالات بهبودیافته
محسن ربانی رضا عربدر این مقاله برای اثبات وجود جواب دستگاه نامتناهی معادلات انتگرال غیرخطی، فضای جواب را فضای شامل همه دنباله‌های همگرا با حد متناهی که با نرم مناسب یک فضای باناخ است در نظر می‌گیریم. با ایجاد تعمیمی ازعملگرهای تراکمی مر - کلر بنام عملگرهای تراکمیF تعمیمیافته مر - کلر[1 چکیده کاملدر این مقاله برای اثبات وجود جواب دستگاه نامتناهی معادلات انتگرال غیرخطی، فضای جواب را فضای شامل همه دنباله‌های همگرا با حد متناهی که با نرم مناسب یک فضای باناخ است در نظر می‌گیریم. با ایجاد تعمیمی ازعملگرهای تراکمی مر - کلر بنام عملگرهای تراکمیF تعمیمیافته مر - کلر[1] و اندازه نافشردگی[2] به اثبات چند قضیه در خصوص وجود نقطه ثابت میپردازیم. با این کارسعی میکنیم بعضی از قضایایی که توسط نویسندگان دیگر [مانند 3, 19] در خصوص وجود جواب بوسیله قضایای نقطه ثابت ارایه شده است را گسترش دهیم. سپس برای اعتبار و کاربرد قضایای پیشنهادیمان، یک نمونه از دستگاه معادلات انتگرال غیرخطی نامتناهی را مورد نظر قرار داده و اثبات وجود جواب آن را به کمک قضایای فوق انجام میدهیم. در آخر برای توانمندی و جذابیت بیشتر این تحقیق، یک الگوریتم تکراری توسط روش هموتوپی اختلالات بهبودیافته و تجزیه ادومین[3] پدید آورده و از آن برای بدست آوردن جواب تقریبی دستگاه نامتناهی معادلات انتگرال غیرخطی فوق استفاده میکنیم. پرونده مقاله -
دسترسی آزاد مقاله
2 - یک روش نیمه تحلیلی بهبود یافته‌ی جدید و سریع برای حل رده‌ای از معادلات انتگرال فوق منفرد نوع دوم
رضا نوین محمد علی فریبرزی عراقی یعقوب محمودیهدف اصلی این تحقیق یافتن جواب تحلیلی رده ای از معادلات انتگرال فوق منفرد نوع دوم به نام پراندتل است که در مباحث فنی من جمله مکانیک پدید می آید. بدین منظور از یک روش بهبود یافته‌ی جدید و سریع بر اساس روش اختلال هموتوپی استفاده می شود. با ارائه‌ی مثال‌هایی نشان خواهیم داد چکیده کاملهدف اصلی این تحقیق یافتن جواب تحلیلی رده ای از معادلات انتگرال فوق منفرد نوع دوم به نام پراندتل است که در مباحث فنی من جمله مکانیک پدید می آید. بدین منظور از یک روش بهبود یافته‌ی جدید و سریع بر اساس روش اختلال هموتوپی استفاده می شود. با ارائه‌ی مثال‌هایی نشان خواهیم داد که روش اختلال هموتوپی استاندارد در حالت کلی برای حل این رده از معادلات انتگرال همگرا نبوده و روش اختلال هموتوپی اصلاح شده نیز صرفاً زمانی همگرا است که جواب دقیق معادله از قبل مشخص باشد، اما روش پیشنهادی در این مقاله، بدون نیاز به دانستنن جواب دقیق مسئله، جواب دقیق این رده از معادلات انتگرال را در دومین تکرار از روش مشخص میکند. نتایج حاصل از مثالها مزایای روش بهبود یافته اختلال هموتوپی جدید را در مقایسه با روشهای استاندارد و اصلاح شده اختلال هموتوپی از جمله سادگی و سرعت بیشتر را نشان می دهد. پرونده مقاله -
دسترسی آزاد مقاله
3 - بعضی از تعمیم های قضیه داربو برای حل یک دستگاه از معادلات انتگرال تابعی با استفاده از اندازه نافشردگی
جمال رضایی روشندر این مقاله با استفاده از مفهوم اندازه نافشردگی، که یک ابزار بسیار مفید و قدرتمند در آنالیز تابعی غیرخطی و نظریه نقطه ثابت متریک و معادلات انتگرال است، یک انقباض جدید در فضای باناخ معرفی میکنیم. برای این منظور با استفاده از یک اندازه نافشردگی روی یک فضای حاصل ضرب مت چکیده کاملدر این مقاله با استفاده از مفهوم اندازه نافشردگی، که یک ابزار بسیار مفید و قدرتمند در آنالیز تابعی غیرخطی و نظریه نقطه ثابت متریک و معادلات انتگرال است، یک انقباض جدید در فضای باناخ معرفی میکنیم. برای این منظور با استفاده از یک اندازه نافشردگی روی یک فضای حاصل ضرب متناهی، تعمیم هایی از قضیه نقطه ثابت داربو بدست میآوریم. آنگاه با استفاده از نتایج حاصله، چند قضیه در وجود زوج نقطه ثابت برای رده‌ای از عملگرها در فضای باناخ ارائه می دهیم. نتایج حاصله بسیاری از نتایج قابل مقایسه را در پیشینه تحقیق بسط و توسعه می دهد. همچنین به عنوان یک کاربرد به مطالعه وجود جواب برای یک رده از دستگاه معادلات انتگرال تابعی غیر خطی میپردازیم که توابع و عملگرها در عملگرهای انتگرال وابسته، در یک شرط انقباض خاص صدق می‌کنند. سرانجام یک مثال ملموس نیز گنجانده شده است که کاربرد نتایج بدست آمده را نشان می‌دهد. پرونده مقاله -
دسترسی آزاد مقاله
4 - حل عددی مدل ریاضی انتشار بیماریهای عفونیبر پایه چندجمله ایهای برنشتاین انتقال یافته
فرشید میرزائی سیده فاطمه حسینی سحر علیپورمعادلات انتگرال ولترا تأخیری کاربرد زیادی در شاخه های مختلف علوم از جمله زیست شناسی، بومشناسی، فیزیک و مدلسازی مسائل مهندسی و علوم طبیعی دارند. در بسیاری از موارد حل تحلیلی این معادلات بسیار دشوار است، بنابراین روشهای عددی به عنوان یک روش تقریبی سودمند برای حل معادلات ا چکیده کاملمعادلات انتگرال ولترا تأخیری کاربرد زیادی در شاخه های مختلف علوم از جمله زیست شناسی، بومشناسی، فیزیک و مدلسازی مسائل مهندسی و علوم طبیعی دارند. در بسیاری از موارد حل تحلیلی این معادلات بسیار دشوار است، بنابراین روشهای عددی به عنوان یک روش تقریبی سودمند برای حل معادلات انتگرال ولترا تأخیری مورد توجه بسیاری از محققین قرار گرفته است. در این مقاله حل عددی معادله انتگرال ولترا- همرشتاین تاخیری با استفاده از روش تقریب کمترین مربعات و بر پایه n برنشتاین انتقال یافته lمورد بحث قرار می گیرد. این معادله یک مدل ریاضی برای انتشار بیماریهای عفونی معینی میباشد که بطور فصلی و با سرعت ثابت تغییر میکند. روش کمترین مربعات مدلی برای برازش داده ها است که در آن مجموع اختلاف بین داده مشاهده شده و مقداری که از مدل بدست می آید کمینه میشود. در این مقاله چندجملهایهای برنشتاین انتقال یافته معرفی شده و سپس تقریب تابعی دلخواه با استفاده از این چندجمله ایها ارائه میگردد. همچنین معادله انتگرال ولترا-همرشتاین تأخیری معرفی میشود و جزئیات روش کمترین مربعات و روش حل مدل ریاضی با روش پیشنهادی بیان میگردد. در پایان دقت و کارایی روش پیشنهادی را با حل دومثال عددی و مقایسه نتایج آنها با دیگر روشهای موجود نشان میدهیم. پرونده مقاله -
دسترسی آزاد مقاله
5 - حل عددی معادلات انتگرال جبری ولترا با روش بسط تیلور
عزیزاله باباخانی الهام انتقامی حسن حسین زادهدر این مقاله با بکارگیری بسط تیلور حل عددی یک دستگاه از معادلات انتگرال جبری تشریح می گردد. این دستگاه معادلات انتگرال جبری شامل تابع مجهول و مشتقاتش می باشد. همچنین تحت شرایطی همگرایی جواب حاصل از این روش به جواب دقیق دستگاه اثبات شده و ضمنا چند مثال برای توصیف این روش چکیده کاملدر این مقاله با بکارگیری بسط تیلور حل عددی یک دستگاه از معادلات انتگرال جبری تشریح می گردد. این دستگاه معادلات انتگرال جبری شامل تابع مجهول و مشتقاتش می باشد. همچنین تحت شرایطی همگرایی جواب حاصل از این روش به جواب دقیق دستگاه اثبات شده و ضمنا چند مثال برای توصیف این روش در تعیین جواب عددی آن و دقت روش مذکور ارائه گردیده است.در این مقاله با بکارگیری بسط تیلور حل عددی یک دستگاه از معادلات انتگرال جبری تشریح می گردد. این دستگاه معادلات انتگرال جبری شامل تابع مجهول و مشتقاتش می باشد. همچنین تحت شرایطی همگرایی جواب حاصل از این روش به جواب دقیق دستگاه اثبات شده و ضمنا چند مثال برای توصیف این روش در تعیین جواب عددی آن و دقت روش مذکور ارائه گردیده است.در این مقاله با بکارگیری بسط تیلور حل عددی یک دستگاه از معادلات انتگرال جبری تشریح می گردد. این دستگاه معادلات انتگرال جبری شامل تابع مجهول و مشتقاتش می باشد. همچنین تحت شرایطی همگرایی جواب حاصل از این روش به جواب دقیق دستگاه اثبات شده و ضمنا چند مثال برای توصیف این روش در تعیین جواب عددی آن و دقت روش مذکور ارائه گردیده است. پرونده مقاله -
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6 - Solving Fuzzy Integral Equations of the Second Kind by using the Reproducing Kernel Hilbert Space Method
صدیقه فرزانه جوان سعید عباسبندی محمدعلی فریبرزی عراقیIn this study, a new approach based on the Reproducing Kernel Hilbert Space Method is proposed to approximate the solution of the second kind fuzzy linear integral equations. For this purpose, at first by applying the concept of parametric form, the fuzzy integral equat چکیده کاملIn this study, a new approach based on the Reproducing Kernel Hilbert Space Method is proposed to approximate the solution of the second kind fuzzy linear integral equations. For this purpose, at first by applying the concept of parametric form, the fuzzy integral equation is converted to a system of crisp integral equations. Then, this system is solved by using the reproducing kernel method free of the Gram-Schmidt orthogonalization process. Also, two numerical algorithms are proposed based on applying the Gram-Schmidt process and without using it. The general form of numerical solution accordingly the reproducing kernel method is introduced and the convergence theorem of solution of the proposed scheme to the exact solution is proved. Finally, a sample fuzzy integral equation is solved by means of both suggested algorithms and the results are compared for differents points and levels. Due to the difficulties in applying the Gram-Schmidt process, the obtained results of the new algorithm are satisfactory. پرونده مقاله -
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7 - کاربرد روش تابع هسته برای حل یک کلاس از معادلات انتگرال خطی دو بعدی با هسته منفرد ضعیف
محمد رضا اصلاحچی مریم رضاییدر این مقاله، یک روش برای حل یک کلاس از معادله انتگرال ولترای خطی دو بعدی نوع دوم با هسته منفرد ضعیف از نوع آبل در فضای هسته‌ی باز تولید شده، ارائه میکنیم. این تابع هسته‌ی باز تولید شده در جزئیات بحث شده است. منفردی ضعیف مساله با بکارگیری انتگرال‌گیری جزء به جزء رفع می چکیده کاملدر این مقاله، یک روش برای حل یک کلاس از معادله انتگرال ولترای خطی دو بعدی نوع دوم با هسته منفرد ضعیف از نوع آبل در فضای هسته‌ی باز تولید شده، ارائه میکنیم. این تابع هسته‌ی باز تولید شده در جزئیات بحث شده است. منفردی ضعیف مساله با بکارگیری انتگرال‌گیری جزء به جزء رفع میشود. علاوه بر این، انتگرال ناسره متعلق به فضای (L_2 (Ω میباشد. در روش ما، جواب دقیق (ϕ(x,t به صورت سری در فضای هسته‌ی باز تولید شده (W(ω نمایش داده میشود و جواب تقریبی (ϕ_n (x,t از طریق قطع کردن n جمله اول سری ساخته میشود. و در ادامه آنالیز همگرایی روش ثابت میشود. همچنین تعدادی مثالهای عددی که برای نشان دادن کارایی و صحت روش ارائه شده‌‌اند، مطالعه می‌شوند. نتایج بدست آمده نشان می‌دهد که خطای جواب تقریبی، در مفهوم نرم فضای (W(ω، وقتی که تعداد نقاط افزایش می‌یابد، یکنوای نزولی است، همچنین نشان می دهد که روش ساده و کاراست. پرونده مقاله -
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8 - حل معادلات انتگرال ولترای تصادفی به روش شبکه عصبی مصنوعی فازی
هادی ابطحی حمیدرضا رحیمی مریم مصلحمعادلات انتگرال ولترا به عنوان خروجی مسائل مطرح شده در علوم پایه و مهندسی کاربر ویژه در پیشبرد حل مسائل پیچیده دارند. یکی از انواع پرکاربرد که متشکل از یک فرایند تصادفی تحت حرکت برونی ایجاد میشود، معادلات انتگرال ولترا تصادفی است. حل این نوع از معادلات همواره از چالش‌ه چکیده کاملمعادلات انتگرال ولترا به عنوان خروجی مسائل مطرح شده در علوم پایه و مهندسی کاربر ویژه در پیشبرد حل مسائل پیچیده دارند. یکی از انواع پرکاربرد که متشکل از یک فرایند تصادفی تحت حرکت برونی ایجاد میشود، معادلات انتگرال ولترا تصادفی است. حل این نوع از معادلات همواره از چالش‌های محقیقن بوده است. از سوی دیگر با توسعه هوش مصنوعی و ارائه روش شبکه عصبی مصنوعی فازی به عنوان یک مدل الهام گرفته از فرایند تفکر و تجزیه و تحلیل در مغز انسان، مدل‌های پیشرفته ای از الگوریتم‌های طراحی شده است. برخی از این این الگوریتم‌های یادگیری در شبکه عصبی مصنوعی فازی در حل معادلات اسفاده شده است . در این مقاله با استفاده از این روش و طراحی یک الگوریتم یادگیری به حل معادلات انتگرال از نوع ولترای تصادفی میپردازیم. روش ارائه شده در این مقاله علاوه بر داشتن دقت بالاتر نسبت به روشهای پیشین، سرعت بیشتری در حل مسئله را دارا است. این موضوع سبب ایجاد یک سطح اطمینان قابل قبول برای محققان در زمان برخورد با این نوع مسائل میشود. پرونده مقاله -
دسترسی آزاد مقاله
9 - پایداری معادلات دیفرانسیل غیر کراندار در فضاهای k- نرم دار فازی به روش نقطه ثابت
معصومه مددی ماهانی رضا سعادتیابتدا فضای k- نرم دار فازی را با کمک نرم های مثلثی و مجموعه های فازی معرفی کرده و سپس پایداری رده ای از معادلات دیفرانسیل را مورد بحث قرار می دهیم. روش مورد استفاده در این مقاله استفاده از قضیه نقطه ثابت می باشد. استفاده از روش نقطه ثابت برای بررسی پایداری معادلات تابعی چکیده کاملابتدا فضای k- نرم دار فازی را با کمک نرم های مثلثی و مجموعه های فازی معرفی کرده و سپس پایداری رده ای از معادلات دیفرانسیل را مورد بحث قرار می دهیم. روش مورد استفاده در این مقاله استفاده از قضیه نقطه ثابت می باشد. استفاده از روش نقطه ثابت برای بررسی پایداری معادلات تابعی در فضاهای نرمدار و فضاهای نرمدار تصادفی اولین بار توسط رادو معرفی شده است. در این مقاله به بررسی معادلات دیفرانسیل((υ^ʹ (ν)=Г(ν, υ(ν میپردازیم که معادله انتگرالی معادله دیفرانسیل فوق به صورت زیر استυ(ν)=υ(m)-∫_m^ν▒Г(τ,υ(τ))dτ.در این مقاله معادله ی شبه انتگرالی برگرفته از معادله دیفرانسیل فوق را به وسیله تابع فازی تحت کنترل قرار میدهیم تا پایدار شود و در نهایت با استفاده از روش نقطه ثابت یک تقریب برای معادله شبه انتگرالی بدست میآوریم. این نتایج پایداری هایزر- اولام راسیاس و پایداری هایزر- اولام را در فضاهای k - نرم دار فازی به روش نقطه ثابت مورد مطالعه قرار می دهد. پرونده مقاله -
دسترسی آزاد مقاله
10 - حل معادله انتگرال ولترای نوع دوم خطی یک بعدی در فضای هسته بازتولید
عباس فضلی شهنام جوادیدر این مقاله یک معادله انتگرال ولترای نوع دوم خطی یک بعدی را حل می­کنیم. بدین منظور با استفاده از شکل معادله، یک عملگر خطی تعریف می­کنیم و با استفاده از آن و عملگر الحاقی­اش و توابع هسته باز تولید یک پایه برای فضای توابع به دست می­آوریم. سپس جواب معادله چکیده کاملدر این مقاله یک معادله انتگرال ولترای نوع دوم خطی یک بعدی را حل می­کنیم. بدین منظور با استفاده از شکل معادله، یک عملگر خطی تعریف می­کنیم و با استفاده از آن و عملگر الحاقی­اش و توابع هسته باز تولید یک پایه برای فضای توابع به دست می­آوریم. سپس جواب معادله انتگرال را بر حسب این توابع پایه­ای به دست می­آوریم. مثال­های ارائه شده در این مقاله صحت و اعتبار روش را نشان می­دهند. اما این روش برای معادلات انتگرال ولترای نوع دوم غیر خطی یک بعدی نتیجه­ای به دست نمی­دهد، در این حالت یک روش جدید برای محاسبه ضرایب فوریه بایستی ارائه شود بنابراین تمرکز بعدی ما ارائه یک روش برای محاسبه ضرایب فوریه در حالت غیر خطی است. این روش به راحتی قابل تعمیم برای معادله انتگرال ولترای نوع دوم خطی دو بعدی است و ما روی این موضوع در مقاله دیگر کار می­کنیم. پرونده مقاله -
دسترسی آزاد مقاله
11 - روش مش لس برای مسئله کنترل بهینه معادلات انتگرال ولترا با استفاده از توابع پایه شعاعی چند درجه دو
ژینوس نظری مله هما الماسیهدر این مقاله، یک روش عددی برای حل مسئله کنترل بهینه معادلات انتگرال ولترا پیشنهاد می شود که این روش تقریب تابع مجهول را با استفاده از توابع پایه شعاعی شامل چند درجه دوها نتیجه می دهد. در واقع با استفاده از درونیابی، بردار کنترل و بردار حالت در دستگاه دینامیکی خطی به گون چکیده کاملدر این مقاله، یک روش عددی برای حل مسئله کنترل بهینه معادلات انتگرال ولترا پیشنهاد می شود که این روش تقریب تابع مجهول را با استفاده از توابع پایه شعاعی شامل چند درجه دوها نتیجه می دهد. در واقع با استفاده از درونیابی، بردار کنترل و بردار حالت در دستگاه دینامیکی خطی به گونه ای تقریب زده می شوند که تابعی هزینه درجه دو مینیمم شود. همچنین برای دقت بیشتر، انتگرالهای موجود در معادله انتگرال ولترا و تابعی هزینه، با استفاده از قاعده انتگرال گیری گاوس-لوباتو-لژاندر تقریب زده می شوند و از نقاط گاوس-لوباتو-لژاندر به عنوان نقاط گره در روش هم محلی استفاده می شود. مسئله کنترل بهینه به یک مسئله مینیمم سازی تبدیل می شود که عناصر بردارهای حالت و کنترل به عنوان تقریبی از بردارهای جواب بر حسب توابع پایه شعاعی هستند. برای بررسی کارایی و دقت روش پیشنهاد شده، نتایج عددی بدست آمده در دو مثال با مقادیر دقیق مقایسه می شوند. پرونده مقاله -
دسترسی آزاد مقاله
12 - نقطه ثابت دوتایی در فضاهای متریک مخروطی مرتب و کاربرد آن در معادلات انتگرال
سمانه قدس مجید اسحاقی گرجیستند پرداخته و سپس یکتایی این نقاط ثابت دوتایی را تحت شرایطی اثبات می نماییم. در قضایای مذکور فضاهای متریک مخروطی مرتب، لزوما نرمال نیستند؛ و در پایان به بیان کاربردی از نتایج اصلی در معادله انتگرال می پردازیم. با وجود آنکه دوو در مقاله[W‎. ‎S‎. ‎Du‎ چکیده کاملستند پرداخته و سپس یکتایی این نقاط ثابت دوتایی را تحت شرایطی اثبات می نماییم. در قضایای مذکور فضاهای متریک مخروطی مرتب، لزوما نرمال نیستند؛ و در پایان به بیان کاربردی از نتایج اصلی در معادله انتگرال می پردازیم. با وجود آنکه دوو در مقاله[W‎. ‎S‎. ‎Du‎, ‎A note on cone metric fixed point theory and its equivalence‎, ‎Nonlinear Analysis‎, ‎72(2010) 2259-2261.]نشان داد که نتایج نقطه ثابت در فضاهای متریک مخروطی دارای خاصیت انقباض خطی در فضاهای متریک برقرار است، اما دوو در مقاله[W‎. ‎S‎. ‎Du, New cone fixed point theorems for nonlinear multivalued maps with their applications‎, ‎Applied Mathematic Letters‎,‎24(2011)172-178]و همچنین جانکوویچ و همکاران در مقاله[S‎. ‎Jankovic‎, ‎Z‎. ‎Kadelburg‎, ‎S‎. ‎Radenovic‎, ‎On cone metric spaces‎: ‎A survey‎, ‎Nonlinear Analysis, ‎74(2011) 2591-2601‎. ]ثابت کردند که هرگاه فضاهای متریک مخروطی غیر نرمال باشند، قضایای فضای متریک ممکن است برقرار نباشند. نتایج این مقاله به این دسته از فضاها اختصاص دارد. در این مقاله ابتدا به اثبات برخی از قضایای نقطه ثابت دوتایی در فضاهای متریک مخروطی مرتب جزئی بر نگاشت­هایی که دارای خاصیت یکنوای آمیخته هستند پرداخته و سپس یکتایی این نقاط ثابت دوتایی را تحت شرایطی اثبات می­نماییم. در قضایای مذکور فضاهای متریک مخروطی مرتب، لزوماً نرمال نیستند؛ و در پایان به بیان کاربردی از نتایج اصلی در معادله انتگرال می­پردازیم. با وجود آنکه دوو در مقاله [W‎. ‎S‎. ‎Du‎, ‎A note on cone metric fixed point theory and its equivalence‎, ‎Nonlinear Analysis‎, ‎72(2010) 2259-2261.] نشان داد که نتایج نقطه ثابت در فضاهای متریک مخروطی دارای خاصیت انقباض خطی در فضاهای متریک برقرار است، اما دوو در مقاله [W‎. ‎S‎. ‎Du, New cone fixed point theorems for nonlinear multivalued maps with their applications‎, ‎Applied Mathematic Letters‎,‎24(2011)172-178] و همچنین جانکوویچ و همکاران در مقاله [S‎. ‎Jankovic‎, ‎Z‎. ‎Kadelburg‎, ‎S‎. ‎Radenovic‎, ‎On cone metric spaces‎: ‎A survey‎, ‎Nonlinear Analysis, ‎74(2011) 2591-2601‎. ] ثابت کردند که هرگاه فضاهای متریک مخروطی غیرنرمال باشند، قضایای فضای متریک ممکن است برقرار نباشند. نتایج این مقاله به این دسته از فضاها اختصاص دارد. پرونده مقاله -
دسترسی آزاد مقاله
13 - A solution for Volterra Integral Equations of the First Kind Based on Bernstein Polynomials
M. Mohamadi E. Babolian S. YousefiIn this paper, we present a new computational method to solve Volterra integral equations of the first kind based on Bernstein polynomials. In this method, using operational matrices turn the integral equation into a system of equations. The computed operational matrice چکیده کاملIn this paper, we present a new computational method to solve Volterra integral equations of the first kind based on Bernstein polynomials. In this method, using operational matrices turn the integral equation into a system of equations. The computed operational matrices are exact and new. The comparisons show this method is acceptable. Moreover, the stability of the proposed method is studied. پرونده مقاله -
دسترسی آزاد مقاله
14 - A Fast and Accurate Expansion-Iterative Method for Solving Second Kind Volterra Integral Equations
S. Hatamzadeh-Varmazyar Z. MasouriThis article proposes a fast and accurate expansion-iterative method for solving second kind linear Volterra integral equations. The method is based on a special representation of vector forms of triangular functions (TFs) and their operational matrix of integration. By چکیده کاملThis article proposes a fast and accurate expansion-iterative method for solving second kind linear Volterra integral equations. The method is based on a special representation of vector forms of triangular functions (TFs) and their operational matrix of integration. By using this approach, solving the integral equation reduces to solve a recurrence relation. The approximate solution of integral equation is iteratively produced via the recurrence relation. پرونده مقاله -
دسترسی آزاد مقاله
15 - B-spline Method for Solving Fredholm Integral Equations of the First Kind
KH. Maleknejad Y. Rostami‎‎‎In this paper‎, we use the collocation method for to find an approximate solution of the problem by cubic B-spline basis.‎ The proposed method as a basic function led matrix systems, including band matrices and smoothness and capability to handle چکیده کامل‎‎‎In this paper‎, we use the collocation method for to find an approximate solution of the problem by cubic B-spline basis.‎ The proposed method as a basic function led matrix systems, including band matrices and smoothness and capability to handle low calculative costly. ‎The absolute errors in the solution are compared to existing methods to verify the accuracy and convergent nature of proposed ‎method. پرونده مقاله -
دسترسی آزاد مقاله
16 - The Use of Fuzzy Variational Iteration Method For Solving Second-Order Fuzzy Abel-Volterra Integro-Differential Equations
S. Sadigh BehzadiIn this paper, fuzzy variational iteration method (FVIM) is proposed to solve the second- order fuzzy Abel-Volterra integro-differential equations. The existence and uniqueness of the solution and convergence of the proposed method are proved in details. is investigated چکیده کاملIn this paper, fuzzy variational iteration method (FVIM) is proposed to solve the second- order fuzzy Abel-Volterra integro-differential equations. The existence and uniqueness of the solution and convergence of the proposed method are proved in details. is investigated to verify convergence results and to illustrate the efficiently of the method. پرونده مقاله -
دسترسی آزاد مقاله
17 - Application of Fuzzy Bicubic Splines Interpolation for Solving Two-Dimensional Linear Fuzzy Fredholm Integral Equations
H. ‎Nouriani‎ R. ‎Ezzati‎‎‎‎In this paper‎, ‎firstly‎, ‎we review approximation of fuzzy functions‎ ‎by fuzzy bicubic splines interpolation and present a new approach‎ ‎based on the two-dimensional fuzzy splines interpolation and‎ ‎iterative method to a چکیده کامل‎In this paper‎, ‎firstly‎, ‎we review approximation of fuzzy functions‎ ‎by fuzzy bicubic splines interpolation and present a new approach‎ ‎based on the two-dimensional fuzzy splines interpolation and‎ ‎iterative method to approximate the solution of two-dimensional‎ ‎linear fuzzy Fredholm integral equation (2DLFFIE)‎. ‎Also‎, ‎we prove‎ ‎convergence analysis and numerical stability analysis for the‎ ‎proposed numerical algorithm‎. ‎Finally‎, ‎by an example‎, ‎we show the‎ ‎efficiency of the proposed ‎method.‎ پرونده مقاله -
دسترسی آزاد مقاله
18 - Numerical Solution of Second Kind Volterra and Fredholm Integral Equations Based on a Direct Method Via Triangular Functions
S. Hatamzadeh-Varmazyar Z. MasouriA numerical method for solving linear integral equations of the second kind is formulated. Based on a special representation of vector forms of triangular functions and the related operational matrix of integration, the integral equation reduces to a linear system of al چکیده کاملA numerical method for solving linear integral equations of the second kind is formulated. Based on a special representation of vector forms of triangular functions and the related operational matrix of integration, the integral equation reduces to a linear system of algebraic equations. Generation of this system needs no integration, so all calculations can easily be implemented. Numerical results for some examples show that the method has a good accuracy. پرونده مقاله -
دسترسی آزاد مقاله
19 - A Method for Numerical Solution of Third-Kind Volterra Integral Equations Using Krall-Laguerre Polynomials
P. Jami E. HashemizadehThe numerical solution of linear integral equations of third kind is discussed in various studies, but in the previous researches on this kind of equations only the analytical solution was investigated. Due to some limitations for this kind of solutions, in this paper w چکیده کاملThe numerical solution of linear integral equations of third kind is discussed in various studies, but in the previous researches on this kind of equations only the analytical solution was investigated. Due to some limitations for this kind of solutions, in this paper we propose a new method for numerical solution of linear integral equations of third kind. The proposed method is based on the approximation of the unknown function with Krall-Laguerre polynomials. This method has a simple computation with a quite acceptable approximate solution. Moreover, we obtain an estimate of the error bound for suggested method. Two examples are also presented to show the efficiency of the proposed method. پرونده مقاله -
دسترسی آزاد مقاله
20 - Solution of Nonlinear Fredholm-Volterra Integral Equations via Block-Pulse Functions
F. Abbasi M. MohamadiIn this paper, a new simple direct method to solve nonlinear Fredholm-Volterra integral equations is presented. By using Block-pulse (BP) functions, their operational matrices and Taylor expansion a nonlinear Fredholm-Volterra integral equation converts to a nonlinear s چکیده کاملIn this paper, a new simple direct method to solve nonlinear Fredholm-Volterra integral equations is presented. By using Block-pulse (BP) functions, their operational matrices and Taylor expansion a nonlinear Fredholm-Volterra integral equation converts to a nonlinear system. Some numerical examples illustrate accuracy and reliability of our solutions. Also, effect of noise shows our solutions are stable. پرونده مقاله -
دسترسی آزاد مقاله
21 - Coincidence and Common Fixed Point Results for $\alpha$-$(\psi,\varphi)$-Contractive Mappings in Metric Spaces
J. Esmaily S. M. Vaezpour R. Saadati‎‎‎Recently Samet et al. introduced the notion of $\alpha$-$\psi$-contractive type mappings and established some fixed point theorems in complete metric spaces. In this paper, we introduce $\alpha$-$(\psi,\varphi)$-contractive mappings and stablish coinciden چکیده کامل‎‎‎Recently Samet et al. introduced the notion of $\alpha$-$\psi$-contractive type mappings and established some fixed point theorems in complete metric spaces. In this paper, we introduce $\alpha$-$(\psi,\varphi)$-contractive mappings and stablish coincidence and common fixed point theorems for two mapping in complete metric spaces. We present some examples to illustrate our results. As application, we establish an existence and uniqueness theorem for a solution of some integral ‎equations.‎ پرونده مقاله -
دسترسی آزاد مقاله
22 - Solving Volterra Integral Equations of the Second Kind with Convolution Kernel
M. S. Barikbin A. R. Vahidi T. ِDamercheliIn this paper, we present an approximate method to solve the solution of the second kind Volterra integral equations. This method is based on a previous scheme, applied by Maleknejad ‎et al., ‎‎[K. Maleknejad ‎and Aghazadeh, Numerical solution of Volterr چکیده کاملIn this paper, we present an approximate method to solve the solution of the second kind Volterra integral equations. This method is based on a previous scheme, applied by Maleknejad ‎et al., ‎‎[K. Maleknejad ‎and Aghazadeh, Numerical solution of Volterra integral equations of the second kind with convolution kernel by using Taylor-series expansion method, ‎Appl. Math. Comput.‎ (2005)]‎ to gain the approximate solution of the second kind Volterra integral equations with convolution kernel and Maleknejad ‎et al. ‎[K. Maleknejad ‎and‎ T. Damercheli, Improving the accuracy of solutions of the linear second kind volterra integral equations system by using the Taylor expansion method, ‎Indian J. Pure Appl. Math.‎ (2014)] ‎to gain the approximate solutions of systems of second kind Volterra integral equations with the help of Taylor expansion method. The Taylor expansion method transforms the integral equation into a linear ordinary differential equation (ODE) which, in this case, requires specified boundary conditions. Boundary conditions can be determined using the integration technique instead of differentiation technique. This method is more stable than derivative method and can be implemented to obtain an approximate solution of the Volterra integral equation with smooth and weakly singular kernels. An error analysis for the method is provided. A comparison between our obtained results and the previous results is made which shows that the suggested method is accurate enough and more ‎stable.‎ پرونده مقاله -
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23 - Numerical Solution of Interval Volterra-Fredholm-Hammerstein Integral Equations via Interval Legendre Wavelets Method
N. khorrami A. Salimi Shamloo B. Parsa MoghaddamIn this paper, interval Legendre wavelet method is investigated to approximated the solution of the interval Volterra-Fredholm-Hammerstein integral equation. The shifted interval Legendre polynomials are introduced and based on interval Legendre wavelet method is define چکیده کاملIn this paper, interval Legendre wavelet method is investigated to approximated the solution of the interval Volterra-Fredholm-Hammerstein integral equation. The shifted interval Legendre polynomials are introduced and based on interval Legendre wavelet method is defined. The existence and uniqueness theorem for the interval Volterra-Fredholm-Hammerstein integral equations is proved. Some examples show the effectiveness and efficiency of the approach. پرونده مقاله -
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24 - Using New Operational Matrix for Solving Nonlinear Fractional Integral Equations
F. Saleki R. ٍٍEzzatiIn this paper, a numerical method for solving nonlinear fractional integral equations (NFIE) is introduced. This method is based on the new basis functions (NFs) introduced in [M. Paripour and et al., Numerical solution of nonlinear Volterra Fredholm integral equations چکیده کاملIn this paper, a numerical method for solving nonlinear fractional integral equations (NFIE) is introduced. This method is based on the new basis functions (NFs) introduced in [M. Paripour and et al., Numerical solution of nonlinear Volterra Fredholm integral equations by using new basis functions, Communications in Numerical Analysis, (2013)]. Since the conventional operational matrices for fractional kernels are singular, the definition of these matrices is modified. In order to increase the accuracy of approximating integrals, the operational matrices are exactly calculated and parametrically presented. Then, the solution procedure is proposed and applied on NFIE. Furthermore, the error analysis is performed and rate of convergence is obtained. In addition, various numerical examples are provided for a wide range of fractional orders and nonlinearity of integral equations. Comparison of the results with the exact solutions and those reported in previous studies indicate the capability, salient accuracy, and superiority of the proposed method over similar ones. پرونده مقاله -
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25 - On the Modified Block-Pulse Function for Volterra Integral Equation of The First Kind
M. Mohammadi A. R. Vahidi T. Damercheli S. Khezerloo M. NouriIn this paper, we consider Volterra integral equations of the first kind. Then by extending the modified Block-pulse functions(MBPFs) on the Volterra integral equation of the second kind obtained from Volterra integral equation of the first kind, we obtain the approxima چکیده کاملIn this paper, we consider Volterra integral equations of the first kind. Then by extending the modified Block-pulse functions(MBPFs) on the Volterra integral equation of the second kind obtained from Volterra integral equation of the first kind, we obtain the approximate solution. Some theorems are proved to provide an error analysis for proposed method. Numerical examples show that the proposed scheme has a suitable degree of accuracy. پرونده مقاله -
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26 - A New Method for Solving Multi-Dimensional Fredholm Integral Equations and Its Convergence Analysis
N. Mahmoodi ‎Darani‎In this paper, we focus on obtaining an approximate solution for multi-dimensional Fredholm integral equations of second kind. An expansion method is used for treatment multi-dimensional Fredholm integral equation of second kind. This method reduces multi-dimensional in چکیده کاملIn this paper, we focus on obtaining an approximate solution for multi-dimensional Fredholm integral equations of second kind. An expansion method is used for treatment multi-dimensional Fredholm integral equation of second kind. This method reduces multi-dimensional integral equation to a partial differential equation. After constructing boundary conditions, this partial differential equation reduces to algebraic equation that can be solved easily with any of the usual methods. Furthermore some theorems are proved for convergence analysis. Finally, for showing the efficiency of the method we use some numerical examples پرونده مقاله -
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27 - A New Efficient Method for Solving System of Fuzzy Volterra Integral Equations Based on Fibonacci Polynomials
T. Sheverini M. Paripour N. KaramikabirHere, based on the Fibonacci polynomials, a new collocation method is presented in order to solve the system of linear fuzzy Volterra integral equations of the second kind. By using this method, these systems are reduced to a linear system of algebraic equations that ar چکیده کاملHere, based on the Fibonacci polynomials, a new collocation method is presented in order to solve the system of linear fuzzy Volterra integral equations of the second kind. By using this method, these systems are reduced to a linear system of algebraic equations that are easily solvable. Also, the existence of the solution and error analysis of the proposed method are discussed. Finally, in order to show the importance and application of the proposed method, we have used several illustrative examples. The method is computationally very attractive and gives very accurate results. Easy implementation and simple operations are the essential features of the Fibonacci polynomials. پرونده مقاله -
دسترسی آزاد مقاله
28 - A Hybrid Approach for Systems of Integral Equations
J. Biazar Y. Parvari Moghaddam kh. Sadri‎In this paper‎, ‎we present a computational method for solving systems of Volterra and Fredholm integral equations which is a hybrid approach‎, ‎based on the third-order Chebyshev polynomials and block-pulse functions which we will refer to as (HBV) چکیده کامل‎In this paper‎, ‎we present a computational method for solving systems of Volterra and Fredholm integral equations which is a hybrid approach‎, ‎based on the third-order Chebyshev polynomials and block-pulse functions which we will refer to as (HBV)‎, ‎for short‎. ‎The existence and uniqueness of the solutions are addressed‎. ‎Some examples are provided to clarify the efficiency and accuracy of the method‎. پرونده مقاله -
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29 - On the Solution of Volterra-Fredholm Integro-Differential Equation by Using New Iterative Method
A. JafarianIntegro-differential equations arise in various physical and biological problems. In this paper, a new iterative technique for solving linear Volterra-Fredholm integro-differential equation (VFIDE) has been introduced. The method is discussed in details and it is illust چکیده کاملIntegro-differential equations arise in various physical and biological problems. In this paper, a new iterative technique for solving linear Volterra-Fredholm integro-differential equation (VFIDE) has been introduced. The method is discussed in details and it is illustrated by solving some numerical examples. The approximate solution is most easily produced iteratively via the recurrence relation. Results are compared with the exact solutions, which reveal that new iteration method is very effective and convenient. پرونده مقاله -
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30 - A New Approach for Solving Volterra Integral Equations Using The Reproducing Kernel Method
R. Ketabchi‎ R. Mokhtari E. BabolianThis paper is concerned with a technique for solving Volterra integral equations in the reproducing kernel Hilbert space. In contrast with the conventional reproducing kernel method, the Gram-Schmidt process is omitted here and satisfactory results are obtained.The anal چکیده کاملThis paper is concerned with a technique for solving Volterra integral equations in the reproducing kernel Hilbert space. In contrast with the conventional reproducing kernel method, the Gram-Schmidt process is omitted here and satisfactory results are obtained.The analytical solution is represented in the form of series.An iterative method is given to obtain the approximate solution.The convergence analysis is established theoretically. The applicability of the iterative method is demonstrated by testing some various ‎examples. پرونده مقاله -
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31 - Numerical solution of the system of Volterra integral equations of the first kind
A. Armand Z. GouyandehThis paper presents a comparison between variational iteration method (VIM) and modfied variational iteration method (MVIM) for approximate solution a system of Volterra integral equation of the first kind. We convert a system of Volterra integral equations to a system چکیده کاملThis paper presents a comparison between variational iteration method (VIM) and modfied variational iteration method (MVIM) for approximate solution a system of Volterra integral equation of the first kind. We convert a system of Volterra integral equations to a system of Volterra integro-di®erential equations that use VIM and MVIM to approximate solution of this system and hence obtain an approximation for system of Volterra integral equations. Some examples are given to show the pertinent features of this methods. پرونده مقاله -
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32 - Theory of block-pulse functions in numerical solution of Fredholm integral equations of the second kind
A. Abdollahi E. BabolianRecently, the block-pulse functions (BPFs) are used in solving electromagnetic scattering problem, which are modeled as linear Fredholm integral equations (FIEs) of the second kind. But the theoretical aspect of this method has not fully investigated yet. In this articl چکیده کاملRecently, the block-pulse functions (BPFs) are used in solving electromagnetic scattering problem, which are modeled as linear Fredholm integral equations (FIEs) of the second kind. But the theoretical aspect of this method has not fully investigated yet. In this article, in addition to presenting a new approach for solving FIE of the second kind, the theory of both methods is investigated as a main part. By providing a new method based on BPFs for solving FIEs of the second kind, the least squares and non-least squares solutions are defined for this problem. First, the convergence of the non-least squares solution is proved by the Nystr$\ddot{o}$m method. ‎T‎hen, considering the fact that the set of all invertible matrices is an open set, the convergence of the least squares solution is investigated. The convergence of Nystr$\ddot{o}$m method has the main role in proving the basic results. Because the presented convergence trend is independent of the orthogonality of the basis functions, the given method can be applied for any arbitrary ‎method.‎ پرونده مقاله -
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33 - Homotopy approximation technique for solving nonlinear Volterra-Fredholm integral equations of the first kind
SH. Sadigh ‎BehzadiIn this paper, a nonlinear Volterra-Fredholm integral equation of the first kind is solved by using the homotopy analysis method (HAM). In this case, the first kind integral equation can be reduced to the second kind integral equation which can be solved by HAM. The app چکیده کاملIn this paper, a nonlinear Volterra-Fredholm integral equation of the first kind is solved by using the homotopy analysis method (HAM). In this case, the first kind integral equation can be reduced to the second kind integral equation which can be solved by HAM. The approximate solution of this equation is calculated in the form of a series which its components are computed easily. The accuracy of the proposed numerical scheme is examined by comparing with other analytical and numerical results. The existence, uniqueness and convergence of the proposed method are proved. Example is presented to illustrate the efficiency and the performance of the homotopy analysis ‎method.‎ پرونده مقاله -
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34 - Mean value theorem for integrals and its application on numerically solving of Fredholm integral equation of second kind with Toeplitz plus Hankel Kernel
N. Mikaeilvand S. Noeiaghdam‎The subject of this paper is the solution of the Fredholm integral equation with Toeplitz, Hankel and the Toeplitz plus Hankel kernel. The mean value theorem for integrals is applied and then extended for solving high dimensional problems and finally, some example چکیده کامل‎The subject of this paper is the solution of the Fredholm integral equation with Toeplitz, Hankel and the Toeplitz plus Hankel kernel. The mean value theorem for integrals is applied and then extended for solving high dimensional problems and finally, some example and graph of error function are presented to show the ability and simplicity of the ‎method. پرونده مقاله -
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35 - Approximation solution of two-dimensional linear stochastic Volterra-Fredholm integral equation via two-dimensional Block-pulse functions
M. Fallahpour‎‎ M. Khodabin‎ K. Maleknejad‎In this paper, a numerical efficient method based on two-dimensional block-pulse functions (BPFs) is proposed to approximate a solution of the two-dimensional linear stochastic Volterra-Fredholm integral equation. Finally the accuracy of this method will be shown by an چکیده کاملIn this paper, a numerical efficient method based on two-dimensional block-pulse functions (BPFs) is proposed to approximate a solution of the two-dimensional linear stochastic Volterra-Fredholm integral equation. Finally the accuracy of this method will be shown by an example. پرونده مقاله -
دسترسی آزاد مقاله
36 - On Optimal Quadrature Rule for Solving Fuzzy Fredholm Integral Equations
R. Ezzati M. M. SadatrasouIn this paper, we present an efficient iterative procedure based on optimal fuzzy quadrature formula to solve fuzzy integral equations. Error estimation and the numerical stability analysis with respect to the choice of the first iteration are given. Some illustrative a چکیده کاملIn this paper, we present an efficient iterative procedure based on optimal fuzzy quadrature formula to solve fuzzy integral equations. Error estimation and the numerical stability analysis with respect to the choice of the first iteration are given. Some illustrative and comparative numerical experiments confirm the optimization of the successive ‎method.‎ پرونده مقاله -
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37 - حل عددی معادلات دیفرانسیل پانتوگراف کسری غیرخطی با شرایط مرزی با استفاده از چندجملهایهای ژاکوبی
سمیه نعمتی فائزه باکوئیدر این پژوهش، یک روش عددی بر پایه‌ی چندجملهایهای ژاکوبی برای حل معادلات دیفرانسیل پانتوگراف کسری غیرخطی با شرایط مرزی معرفی میشود. ابتدا، معادله دیفرانسیل به‌صورت یک معادله انتگرال ولترا-فردهلم معادل بیان میشود. سپس، چندجملهایهای ژاکوبی و فرمول انتگرال‌گیری گاو چکیده کاملدر این پژوهش، یک روش عددی بر پایه‌ی چندجملهایهای ژاکوبی برای حل معادلات دیفرانسیل پانتوگراف کسری غیرخطی با شرایط مرزی معرفی میشود. ابتدا، معادله دیفرانسیل به‌صورت یک معادله انتگرال ولترا-فردهلم معادل بیان میشود. سپس، چندجملهایهای ژاکوبی و فرمول انتگرال‌گیری گاوس-ژاکوبی به‌همراه نقاط هم‌محلی نیوتن-کاتس برای تبدیل معادله انتگرال حاصل به دستگاهی از معادلات جبری غیرخطی استفاده میشود. در آخر، با در نظر گرفتن چند مثال و محاسبه خطاهای L^"2" و L^∞، کارایی و دقت روش پیشنهادی نشان داده میشود.- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - پرونده مقاله -
دسترسی آزاد مقاله
38 - An Axisymmetric Torsion Problem of an Elastic Layer on a Rigid Circular Base
B Kebli S Berkane F GuerracheA solution is presented to a doubly mixed boundary value problem of the torsion of an elastic layer, partially resting on a rigid circular base by a circular rigid punch attached to its surface. This problem is reduced to a system of dual integral equations using the Bo چکیده کاملA solution is presented to a doubly mixed boundary value problem of the torsion of an elastic layer, partially resting on a rigid circular base by a circular rigid punch attached to its surface. This problem is reduced to a system of dual integral equations using the Boussinesq stress functions and the Hankel integral transforms. With the help of the Gegenbauer expansion formula of the Bessel function we get an infinite algebraic system of simultaneous equations for calculating the unknown function of the problem. Both the two contact stresses under the punch and on the lower face of the layer are expressed as appropriate Chebyshev series. The effects of the radius of the disc with the rigid base and the layer thickness on the displacements, contact stresses as well as the shear stress and the stress singularity factor are discussed. A numerical application is also considered with some concluding results. پرونده مقاله -
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39 - Application of Chebyshev Polynomials for Solving Abel's Integral Equations of the First and Second Kind
Ahmad Shahsavaran M. M. ShamivandIn this paper, a numerical implementation of an expansion method is developed for solving Abel's integral equations of the first and second kind. The solution of such equations may demonstrate a singular behaviour in the neighbourhood of the initial point of the interva چکیده کاملIn this paper, a numerical implementation of an expansion method is developed for solving Abel's integral equations of the first and second kind. The solution of such equations may demonstrate a singular behaviour in the neighbourhood of the initial point of the interval ofintegration. The suggested method is based on the use of Taylor series expansion to overcome the singularity which leads to approximating the unknown function and it's derivatives in terms of Chebyshev polynomials of the first kind. The proposed method, transforms the Abel's integral equations of the first and second kind into a system of linear algebraic equations which can be solved by Gaussian elimination algorithm. Finally, some numerical examples are included to clarify the accuracy and applicability of the presented method which indicate that proposed method is computationally very attractive. In thispaper, all numerical computations were carried out on a PC executing some programs written in maple software. پرونده مقاله -
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40 - A meshless technique for nonlinear Volterra-Fredholm integral equations via hybrid of radial basis functions
Jinoos Nazari Homa AlmasiehIn this paper, an effective technique is proposed to determine thenumerical solution of nonlinear Volterra-Fredholm integralequations (VFIEs) which is based on interpolation by the hybrid ofradial basis functions (RBFs) including both inverse multiquadrics(IMQs), hyperb چکیده کاملIn this paper, an effective technique is proposed to determine thenumerical solution of nonlinear Volterra-Fredholm integralequations (VFIEs) which is based on interpolation by the hybrid ofradial basis functions (RBFs) including both inverse multiquadrics(IMQs), hyperbolic secant (Sechs) and strictly positive definitefunctions. Zeros of the shifted Legendre polynomial are used asthe collocation points to set up the nonlinear systems. Theintegrals involved in the formulation of the problems areapproximated based on Legendre-Gauss-Lobatto integration rule.This technique is so convenience to implement and yields veryaccurate results compared with the other basis. In addition aconvergence theorem is proved to show the stability of thistechnique. Illustrated examples are included to confirm thevalidity and applicability of the proposed method. The comparisonof the errors is implemented by the other methods in referencesusing both inverse multiquadrics (IMQs), hyperbolic secant (Sechs)and strictly positive definite functions. پرونده مقاله -
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41 - Spectral Scheme for Solving Fuzzy Volterra Integral Equations of First Kind
Laleh HooshangianThis paper discusses about the solution of fuzzy Volterra integral equation of first-kind (F-VIE1) using spectral method. The parametric form of fuzzy driving term is applied for F-VIE1, then three classifications for (F-VIE1) are searched to solve them. These classific چکیده کاملThis paper discusses about the solution of fuzzy Volterra integral equation of first-kind (F-VIE1) using spectral method. The parametric form of fuzzy driving term is applied for F-VIE1, then three classifications for (F-VIE1) are searched to solve them. These classifications are considered based on the interval sign of the kernel. The Gauss-Legendre points and Legendre weights for arithmetics in spectral method are used to solve (F-VIE1). Finally, two examples are got to illustrate more. However, accuracy and efficiency are shown in tables. \ پرونده مقاله -
دسترسی آزاد مقاله
42 - Spectral method for Solving Fuzzy Volterra Integral Equations of Second kind
Laleh HooshangianThis paper, about the solution of fuzzy Volterra integral equation of fuzzy Volterra integral equation of second kind (F-VIE2) using spectral method is discussed. The parametric form of fuzzy driving term is applied for F-VIE2. Then three cases for (F-VIE2) are searched چکیده کاملThis paper, about the solution of fuzzy Volterra integral equation of fuzzy Volterra integral equation of second kind (F-VIE2) using spectral method is discussed. The parametric form of fuzzy driving term is applied for F-VIE2. Then three cases for (F-VIE2) are searched to solve them. This classifications are considered based on the sign of interval. The Gauss-Legendre points and Legendre weights for arithmetics in spectral method are used to solve (F-VIE2). Finally two examples are got to illustrate more.b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b پرونده مقاله -
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43 - A New Method for Solving Two-Dimensional Fuzzy Fredholm Integral Equations of The Second Kind
Mohsen Darabi Nouredin Parandin Mahmoud Paripour Ali SeifiIn this work, we introduce a novel method for solving two-dimensional fuzzy Fredholm integral equationsof the second kind (2D-FFIE-2). We use new representation of parametric form of fuzzy numbers and converta two-dimensional fuzzy Fredholm integral equation to system o چکیده کاملIn this work, we introduce a novel method for solving two-dimensional fuzzy Fredholm integral equationsof the second kind (2D-FFIE-2). We use new representation of parametric form of fuzzy numbers and converta two-dimensional fuzzy Fredholm integral equation to system of two-dimensional Fredholm integral equationsof the second kind in crisp case. We can use Adomian decomposition method for nding the approximationsolution of the each equation, hence obtain an approximation for fuzzy solution of 2D-FFIE-2. We prove theconvergence of the method and nally apply the method to some examples پرونده مقاله -
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44 - A novel method to solve fuzzy Volterra integral equations using collocation method
Nouredin Parandin Mohsen DarabiFuzzy Volterra integral equations, especially the second kind is interested for researchers to be solved withnumerical methods since analytical methods are not applicable. Here a new study based on Fibonacci polynomialscollocation method in order to solve them is introd چکیده کاملFuzzy Volterra integral equations, especially the second kind is interested for researchers to be solved withnumerical methods since analytical methods are not applicable. Here a new study based on Fibonacci polynomialscollocation method in order to solve them is introduced. Some properties of these polynomials are consideredto implement a collocation method in order to approximate the solution of Fuzzy Volterra integral equations ofthe second kind. The existence and uniqueness of the solution also convergence and error analysis of proposedmethod are proved thoroughly. The results showed the calculations of the method are simple and low cost. پرونده مقاله -
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45 - Using the Finite Differences Method for the Fredholm Integral Equations of the Second Kind
Nooshin Pashmakian Ali Farajzadeh نورالدین پرندینIn this paper, we want to solve the Fredholm integral equations of the second type using thenumerical finite differences method. In this method, we use the forward, central and backwardoperator’s to solve integral equations, and finally we compare these methods wi چکیده کاملIn this paper, we want to solve the Fredholm integral equations of the second type using thenumerical finite differences method. In this method, we use the forward, central and backwardoperator’s to solve integral equations, and finally we compare these methods with the help of nu-merical examples. پرونده مقاله -
دسترسی آزاد مقاله
46 - Spectral Method for Solving Fuzzy Volterra Integral Equations of Second kind
Laleh HooshangianThis paper, about the solution of fuzzy Volterra integral equation of fuzzy Volterra integralequation of second kind (F-VIE2) using spectral method is discussed. The parametric form offuzzy driving term is applied for F-VIE2. Then three cases for (F-VIE2) are searched t چکیده کاملThis paper, about the solution of fuzzy Volterra integral equation of fuzzy Volterra integralequation of second kind (F-VIE2) using spectral method is discussed. The parametric form offuzzy driving term is applied for F-VIE2. Then three cases for (F-VIE2) are searched to solvethem. These classifications are considered based on the sign of interval. The Gauss-Legendrepoints and Legendre weights for arithmetics in spectral method are used to solve (F-VIE2).Finally, two examples are got to illustrate more. پرونده مقاله -
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47 - Using Parametric continuity method for solving Fredholm nonlinear integral equationsution
Majied Babaee Mahmoud Paripour Nasrin KaramikabirThis study is based on the article "Parameter Duration Method for Solving Nonlinear Fredholm Integral Equations of the Second kind "and is collected from the writings of Nineh and Vitkha.In this paper, first, the Fredholm nonlinear integral equation of the second type i چکیده کاملThis study is based on the article "Parameter Duration Method for Solving Nonlinear Fredholm Integral Equations of the Second kind "and is collected from the writings of Nineh and Vitkha.In this paper, first, the Fredholm nonlinear integral equation of the second type is solved using the parametric continuity method. Next, the parametric continuity method is introduced to solve the turbulent nonlinear integral equation of the second type, which is an extension of the paradoxical mapping method. Also, the parametric continuity method is applied to solve the nonlinear integral equation of the second type. Lastly, sample examples are given to show the effectiveness and convenience of the parametric continuity method. پرونده مقاله -
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48 - A Legendre-spectral scheme for solution of nonlinear system of Volterra-Fredholm integral equations
L. Hooshangian D. MirzaieThis paper gives an ecient numerical method for solving the nonlinear systemof Volterra-Fredholm integral equations. A Legendre-spectral method based onthe Legendre integration Gauss points and Lagrange interpolation is proposedto convert the nonlinear integral equatio چکیده کاملThis paper gives an ecient numerical method for solving the nonlinear systemof Volterra-Fredholm integral equations. A Legendre-spectral method based onthe Legendre integration Gauss points and Lagrange interpolation is proposedto convert the nonlinear integral equations to a nonlinear system of equationswhere the solution leads to the values of unknown functions at collocationpoints. پرونده مقاله -
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49 - The combined Sinc-Taylor expansion method to solve Abel's integral equation
M Fariborzi Araghi Gh Kazami-GelianIn this paper , numerical solotion of Abel's integral equationby using the Taylor expanssion of the unknown functionvia collection method based on Sinc is considered...In this paper , numerical solotion of Abel's integral equationby using the Taylor expanssion of the unknown functionvia collection method based on Sinc is considered... پرونده مقاله -
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50 - Legendre wavelet method for solving Hammerstein integral equations of the second kind
Sh Javadi J Saeidian F SafariAn ecient method, based on the Legendre wavelets, is proposed to solve thesecond kind Fredholm and Volterra integral equations of Hammerstein type.The properties of Legendre wavelet family are utilized to reduce a nonlinearintegral equation to a system of nonlinear alg چکیده کاملAn ecient method, based on the Legendre wavelets, is proposed to solve thesecond kind Fredholm and Volterra integral equations of Hammerstein type.The properties of Legendre wavelet family are utilized to reduce a nonlinearintegral equation to a system of nonlinear algebraic equations, which is easilyhandled with the well-known Newton's method. Examples assuring eciencyof the method and its superiority are presented. پرونده مقاله -
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51 - Evaluating the solution for second kind nonlinear Volterra Fredholm integral equations using hybrid method
Ahamd Shahsavaran Akbar ShahsavaranIn this work, we present a computational method for solving second kindnonlinear Fredholm Volterra integral equations which is based on the use ofHaar wavelets. These functions together with the collocation method are thenutilized to reduce the Fredholm Volterra integra چکیده کاملIn this work, we present a computational method for solving second kindnonlinear Fredholm Volterra integral equations which is based on the use ofHaar wavelets. These functions together with the collocation method are thenutilized to reduce the Fredholm Volterra integral equations to the solution ofalgebraic equations. Finally, we also give some numerical examples that showsvalidity and applicability of the technique. پرونده مقاله -
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52 - Numerical Solution of a New Type Fuzzy Nonlinear Volterra Integral Equations
Laleh HooshangianFuzzy integral equations play a fundamental role in the many fields of engineering and applied mathematics.The paper presented, a new type of fuzzy Volterra integral equations of the second kind with nonlinear fuzzykernels. Numerical solutions of a new type of nonlinear چکیده کاملFuzzy integral equations play a fundamental role in the many fields of engineering and applied mathematics.The paper presented, a new type of fuzzy Volterra integral equations of the second kind with nonlinear fuzzykernels. Numerical solutions of a new type of nonlinear fuzzy Volterra integral equations with nonlinear fuzzy kernels through Variational Homotopy perturbation (VHP) method based on the parametric form of a fuzzy number, is investigated. To find the approximate solution and to get an approximation for fuzzy solution of the new type of nonlinear fuzzy Volterra integral equations the VHPM is applied, and it is shown that VHPM is an effective and reliable approach to solve these equations. Finally, a few numerical examples are given and results unfold that VHPM is very close to exact solutions. The obtained approximate solutions are contrasted with the exact solution, and absolute error between obtaining numerical results and an exact solution are found. One of the examples shows a comparison between VHPM and HPM. پرونده مقاله -
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53 - Numerical solution of Hammerstein Fredholm and Volterra integral equations of the second kind using block pulse functions and collocation method
M. M. Shamivand A. ShahsavaranIn this work, we present a numerical method for solving nonlinear Fredholmand Volterra integral equations of the second kind which is based on the useof Block Pulse functions(BPfs) and collocation method. Numerical examplesshow eciency of the method.In this work, we present a numerical method for solving nonlinear Fredholmand Volterra integral equations of the second kind which is based on the useof Block Pulse functions(BPfs) and collocation method. Numerical examplesshow eciency of the method. پرونده مقاله -
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54 - Numerical solution of nonlinear integral equations by Galerkin methods with hybrid Legendre and Block-Pulse functions
M. Tavassoli Kajani S. MahdaviIn this paper, we use a combination of Legendre and Block-Pulse functionson the interval [0; 1] to solve the nonlinear integral equation of the second kind.The nonlinear part of the integral equation is approximated by Hybrid Legen-dre Block-Pulse functions, and the non چکیده کاملIn this paper, we use a combination of Legendre and Block-Pulse functionson the interval [0; 1] to solve the nonlinear integral equation of the second kind.The nonlinear part of the integral equation is approximated by Hybrid Legen-dre Block-Pulse functions, and the nonlinear integral equation is reduced to asystem of nonlinear equations. We give some numerical examples. To showapplicability of the proposed method. پرونده مقاله -
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55 - Analysis of convergence of solution of general fuzzy integral equation with nonlinear fuzzy kernels
Laleh HooshangianFuzzy integral equations have a major role in the mathematics and applications.In this paper, general fuzzy integral equations with nonlinear fuzzykernels are introduced. The existence and uniqueness of their solutions areapproved and an upper bound for them are determi چکیده کاملFuzzy integral equations have a major role in the mathematics and applications.In this paper, general fuzzy integral equations with nonlinear fuzzykernels are introduced. The existence and uniqueness of their solutions areapproved and an upper bound for them are determined. Finally an algorithmis drawn to show theorems better. پرونده مقاله -
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56 - A three-step method based on Simpson's 3/8 rule for solving system of nonlinear Volterra integral equations
M. Tavassoli-Kajani L. Kargaran-Dehkordi Sh. Hadian-JaziThis paper proposes a three-step method for solving nonlinear Volterra integralequations system. The proposed method convents the system to a (3 × 3)nonlinear block system and then by solving this nonlinear system we ndapproximate solution of nonlinear Volterra چکیده کاملThis paper proposes a three-step method for solving nonlinear Volterra integralequations system. The proposed method convents the system to a (3 × 3)nonlinear block system and then by solving this nonlinear system we ndapproximate solution of nonlinear Volterra integral equations system. To showthe advantages of our method some numerical examples are presented. پرونده مقاله -
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57 - Evaluating the solution for second kind nonlinear Volterra Fredholm integral equations using hybrid method
Ahmad Shahsavaran Akbar ShahsavaranIn this work, we present a computational method for solving second kindnonlinear Fredholm Volterra integral equations which is based on the use ofHaar wavelets. These functions together with the collocation method are thenutilized to reduce the Fredholm Volterra integra چکیده کاملIn this work, we present a computational method for solving second kindnonlinear Fredholm Volterra integral equations which is based on the use ofHaar wavelets. These functions together with the collocation method are thenutilized to reduce the Fredholm Volterra integral equations to the solution ofalgebraic equations. Finally, we also give some numerical examples that showsvalidity and applicability of the technique. پرونده مقاله -
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58 - Buckling of Doubly Clamped Nano-Actuators in General form Through Spectral Meshless Radial Point Interpolation (SMRPI)
Hedayat Fatahi Elyas Shivanian S. J. Hosseini GhonchehThe present paper is devoted to the development of a kind of spectral meshless radial point interpolation (SMRPI) technique in order to obtain a reliable approximate solution for buckling of nano-actuators subject to different nonlinear forces. To end this aim, a genera چکیده کاملThe present paper is devoted to the development of a kind of spectral meshless radial point interpolation (SMRPI) technique in order to obtain a reliable approximate solution for buckling of nano-actuators subject to different nonlinear forces. To end this aim, a general type of the governing equation for nano-actuators, containing integro-differential terms and nonlinear forces is considered. This general type for the nano-actuators is a non-linear fourth-order Fredholm integro-differential boundary value problem. The point interpolation method with the help of radial basis functions is used to construct shape functions which play as basis functions in the frame of SMRPI. In the current work, the thin plate splines (TPSs) are used as radial basis functions. This numerical based technique enables us to overcome all kind of nonlinearities in the mentioned boundary value problem and then to obtain fast convergent solution. Thus, it can facilitate the design of nano-actuators. پرونده مقاله -
دسترسی آزاد مقاله
59 - Solving linear and nonlinear Volterra Fuzzy Integral Equations System via Differential Transform Method
Mahmoud Paripour Mandana TakrimiIn this study, we consider solving the second kind Volterra fuzzy integral equations system in two cases linear and nonlinear by using a semi-analytic method, called Differential Transform Method (DTM). In this algorithm the first, we convert a Volterra fuzzy integral e چکیده کاملIn this study, we consider solving the second kind Volterra fuzzy integral equations system in two cases linear and nonlinear by using a semi-analytic method, called Differential Transform Method (DTM). In this algorithm the first, we convert a Volterra fuzzy integral equations system into two crisp integral equations systems of Volterra; then we solve each of them via DTM. If the equation has a solution in terms of the series expansion of known functions; this powerful method will catch the exact solution. Moreover, the ability and efficiency of the algorithm are shown by solving some numerical examples.In this study, we consider solving the second kind Volterra fuzzy integral equations system in two cases linear and nonlinear by using a semi-analytic method, called Differential Transform Method (DTM). In this algorithm the first, we convert a Volterra fuzzy integral equations system into two crisp integral equations systems of Volterra; then we solve each of them via DTM. If the equation has a solution in terms of the series expansion of known functions; this powerful method will catch the exact solution. Moreover, the ability and efficiency of the algorithm are shown by solving some numerical examples. پرونده مقاله -
دسترسی آزاد مقاله
60 - An efficient technique for solving systems of integral equations
حمیده ابراهیمیIn this paper, the wavelet method based on the Chebyshev polynomials of the second kind is introduced and used to solve systems of integral equations. Operational matrices of integration, product, and derivative are obtained for the second kind Chebyshev wavelets which چکیده کاملIn this paper, the wavelet method based on the Chebyshev polynomials of the second kind is introduced and used to solve systems of integral equations. Operational matrices of integration, product, and derivative are obtained for the second kind Chebyshev wavelets which will be used to convert the system of integral equations into a system of algebraic equations. Also, the error is analyzed and at the end, some examples are presented to demonstrate the efficiency and the validity of the proposed method. پرونده مقاله -
دسترسی آزاد مقاله
61 - Numerical solution of Fredholm and Volterra integral equations using the normalized Müntz−Legendre polynomials
فرشته صائمی حمیده ابراهیمی محمود شفیعیThe current research approximates the unknown function based on the normalized Müntz−Legendre polynomials (NMLPs) in conjunction with a spectral method for the solution of nonlinear Fredholm and Volterra integral equations. In this method, by using operationa چکیده کاملThe current research approximates the unknown function based on the normalized Müntz−Legendre polynomials (NMLPs) in conjunction with a spectral method for the solution of nonlinear Fredholm and Volterra integral equations. In this method, by using operational matrices, a system of algebraic equations is derived that can be readily handled through the use of the Newton scheme. The stability, error bound, and convergence analysis of the method are discussed in detail by preparing some theorems. Several illustrative examples are provided formally to show the efficiency of the proposed method. پرونده مقاله -
دسترسی آزاد مقاله
62 - Variational Iteration Method for Fredholm integral equations of the second kind
ج. بی آزار H. ابراهیمیIn this paper, He‘s variational iteration method is applied to Fredholm integral equations of the second kind. To illustrate the ability and simplicity of the method, some examples are provided. The results reveal that the proposed method is very effective and sim چکیده کاملIn this paper, He‘s variational iteration method is applied to Fredholm integral equations of the second kind. To illustrate the ability and simplicity of the method, some examples are provided. The results reveal that the proposed method is very effective and simple and for first fourth examples leads to the exact solution. پرونده مقاله -
دسترسی آزاد مقاله
63 - A numerical solution of mixed Volterra Fredholm integral equations of Urysohn type on non-rectangular regions using meshless methods
M. Nili Ahmadabadi H. Laeli DastjerdiIn this paper, we propose a new numerical method for solution of Urysohn two dimensional mixed Volterra-Fredholm integral equations of the second kind on a non-rectangular domain. The method approximates the solution by the discrete collocation method based on inverse m چکیده کاملIn this paper, we propose a new numerical method for solution of Urysohn two dimensional mixed Volterra-Fredholm integral equations of the second kind on a non-rectangular domain. The method approximates the solution by the discrete collocation method based on inverse multiquadric radialbasis functions (RBFs) constructed on a set of disordered data. The method is a meshless method, because it is independent of the geometry of the domain and it does not require any background interpolation or approximation cells. The error analysisof the method is provided. Numerical results are presented, which confirm the theoretical prediction of the convergence behavior of the proposed method. پرونده مقاله -
دسترسی آزاد مقاله
64 - Numerical solution of a type of weakly singular nonlinear Volterra integral equation by Tau Method
H. Laeli Dastjerdi M. Nili Ahmadabadi‎In this paper‎, ‎a matrix based method is considered for the solution of a class of nonlinear Volterra integral equations with a kernel of the general form $s^{\beta}(t-s)^{-\alpha}G(y(s))$ based on the Tau method‎. ‎In this method‎, ‎a tran چکیده کامل‎In this paper‎, ‎a matrix based method is considered for the solution of a class of nonlinear Volterra integral equations with a kernel of the general form $s^{\beta}(t-s)^{-\alpha}G(y(s))$ based on the Tau method‎. ‎In this method‎, ‎a transformation of the independent variable is first introduced in order to obtain a new equation with smoother solution‎. ‎Error analysis of this method is also presented‎. ‎Some numerical examples are provided to illustrate the accuracy and computational efficiency of the method‎. پرونده مقاله -
دسترسی آزاد مقاله
65 - The method of radial basis functions for the solution of nonlinear Fredholm integral equations system.
J. Nazari M. Nili Ahmadabadi H. AlmasiehIn this paper, An effective and simple numerical method is proposed for solving systems of integral equations using radial basis functions (RBFs). We present an algorithm based on interpolation by radial basis functions including multiquadratics (MQs), using Legendre-Ga چکیده کاملIn this paper, An effective and simple numerical method is proposed for solving systems of integral equations using radial basis functions (RBFs). We present an algorithm based on interpolation by radial basis functions including multiquadratics (MQs), using Legendre-Gauss-Lobatto nodes and weights. Also a theorem is proved for convergence of the algorithm. Some numerical examples are presented and results are compared to the analytical solution and Triangular functions (TF), Delta basis functions (DFs), block-pulse functions , sinc fucntions, Adomian decomposition, computational, Haar wavelet and direct methods to demonstrate the validity and applicability of the proposed method. پرونده مقاله -
دسترسی آزاد مقاله
66 - Hyers–Ulam–Rassias stability of impulsive Volterra integral equation via a fixed point approach
R. Shah A. Zada‎In this paper‎, ‎we establish the Hyers--Ulam--Rassias stability and the Hyers--Ulam stability of impulsive Volterra integral equation by using a fixed point method‎.‎In this paper‎, ‎we establish the Hyers--Ulam--Rassias stability and the Hyers--Ulam stability of impulsive Volterra integral equation by using a fixed point method‎. پرونده مقاله -
دسترسی آزاد مقاله
67 - Fixed point results for Su-type contractive mappings with an application
A. Ali H. Işık F. Uddin M. Arshad‎In this paper‎, ‎we introduce the concept of Su-type contractive mapping and establish fixed point theorems for such mappings in the setting of ordered‎‎extended partial $b$-metric space‎. ‎We also develop an‎‎application for Fredhol چکیده کامل‎In this paper‎, ‎we introduce the concept of Su-type contractive mapping and establish fixed point theorems for such mappings in the setting of ordered‎‎extended partial $b$-metric space‎. ‎We also develop an‎‎application for Fredholm type integral equations to‎‎validate our main result and a non-trivial example is given to‎‎elucidate our work. پرونده مقاله -
دسترسی آزاد مقاله
68 - An efficient method for the numerical solution of functional integral equations
M. Nili AhmadabadiWe propose an efficient mesh-less method for functional integral equations. Its convergence analysis has been provided. It is tested via a few numerical experiments which show the efficiency and applicability of the proposed method. Attractive numerical results have bee چکیده کاملWe propose an efficient mesh-less method for functional integral equations. Its convergence analysis has been provided. It is tested via a few numerical experiments which show the efficiency and applicability of the proposed method. Attractive numerical results have been obtained. پرونده مقاله -
دسترسی آزاد مقاله
69 - Expansion methods for solving integral equations with multiple time lags using Bernstein polynomial of the second kind
M. Paripour Z. Shojaei S. AbdolahiIn this paper, the Bernstein polynomials are used to approximate the solutionsof linear integral equations with multiple time lags (IEMTL) through expansion methods(collocation method, partition method, Galerkin method). The method is discussed in detail and illustrated چکیده کاملIn this paper, the Bernstein polynomials are used to approximate the solutionsof linear integral equations with multiple time lags (IEMTL) through expansion methods(collocation method, partition method, Galerkin method). The method is discussed in detail and illustrated by solving some numerical examples. Comparison between the exact andapproximated results obtained from these methods is carried out. پرونده مقاله -
دسترسی آزاد مقاله
70 - Numerical solution of functional integral equations by using B-splines
R. Firouzdor A. Heidarnejad Khoob Z. MollaramezaniThis paper describes an approximating solution, based on Lagrange interpolationand spline functions, to treat functional integral equations of Fredholm type and Volterra type.This method can be extended to functional differential and integro-differential equations. Fors چکیده کاملThis paper describes an approximating solution, based on Lagrange interpolationand spline functions, to treat functional integral equations of Fredholm type and Volterra type.This method can be extended to functional differential and integro-differential equations. Forshowing efficiency of the method we give some numerical examples. پرونده مقاله -
دسترسی آزاد مقاله
71 - A Note on Solving Prandtl's Integro-Differential Equation
Atta Dezhbord Taher LotfiA simple method for solving Prandtl's integro-differential equation is proposed based on a new reproducing kernel space. Using a transformation and modifying the traditional reproducing kernel method, the singular term is removed and the analytical representation of the چکیده کاملA simple method for solving Prandtl's integro-differential equation is proposed based on a new reproducing kernel space. Using a transformation and modifying the traditional reproducing kernel method, the singular term is removed and the analytical representation of the exact solution is obtained in the form of series in the new reproducing kernel space. Compared with known investigations, its advantages are that the representation of the exact solution is obtained in a reproducing kernel Hilbert space and accuracy in numerical computation is higher. On the other hand, the approximate solution and its derivatives converge uniformly to the exact solution and its derivatives. The final numerical experiments illustrate the method is efficient. پرونده مقاله -
دسترسی آزاد مقاله
72 - Numerical Solution of the Lane-Emden Equation Based on DE Transformation via Sinc Collocation Method
Ghasem Kazemi GelianIn this paper‎, ‎numerical solution of‎ ‎general Lane-Emden equation via collocation method based on‎ ‎Double Exponential DE transformation is considered‎. ‎The‎ ‎method converts equation to the nonlinear Volterra integral‎ &l چکیده کاملIn this paper‎, ‎numerical solution of‎ ‎general Lane-Emden equation via collocation method based on‎ ‎Double Exponential DE transformation is considered‎. ‎The‎ ‎method converts equation to the nonlinear Volterra integral‎ ‎equation‎. ‎Numerical examples show the accuracy of the method.‎ ‎Also‎, ‎some remarks with respect to run-time‎, computational cost‎ ‎and implementation are discussed. پرونده مقاله -
دسترسی آزاد مقاله
73 - Approximate Solution of the Second Order Initial Value Problem by Using Epsilon Modified Block-Pulse Function
Mahnaz Mohammadi Alireza Vahidi Saeid KhezerlooThe present work approaches the problem of achieving the approximate solution of the second order initial value problems (IVPs) via its conversion into a Volterra integral equation of the second kind (VIE2). Therefore, we initially solve the IVPs using Runge–Kutta چکیده کاملThe present work approaches the problem of achieving the approximate solution of the second order initial value problems (IVPs) via its conversion into a Volterra integral equation of the second kind (VIE2). Therefore, we initially solve the IVPs using Runge–Kutta of the forth–order method (RK), and then convert it into VIE2, and apply the εmodified block–pulse functions (εMBPFs) and their operational matrix for solving VIE2, which can be transformed to a lower triangular system of algebric equations. Numerical examples show that the proposed scheme has a suitable degree of accuracy. پرونده مقاله -
دسترسی آزاد مقاله
74 - A New Iterative Method of Successive Approximation to Solve Nonlinear Urysohn Integral Equations by Haar Wavelet
Manochehr Kazemi Vali Torkashvand Einollah FathizadeIn this paper, a new method for calculating the numerical approximation of the nonlinear Urysohn integral equations is proposed based on Haar wavelets. Also, the convergence analysis and numerical stability of these method are discussed. Conducting numerical experiments چکیده کاملIn this paper, a new method for calculating the numerical approximation of the nonlinear Urysohn integral equations is proposed based on Haar wavelets. Also, the convergence analysis and numerical stability of these method are discussed. Conducting numerical experiments confirm the theoretical results of the applied method and endorse the accuracy of the method. پرونده مقاله -
دسترسی آزاد مقاله
75 - Using Radial Basis Functions for Numerical Solving Two-Dimensional Voltrra Linear Functional Integral Equations
reza Firouzdor Neda Khaksary Atousa EmadyThis article is an attempt to obtain the numerical solution of functional linear Voltrra two-dimensional integral equations using Radial Basis Function (RBF) interpolation which isbased on linear composition of terms. By using RBF in functional integral equation, rst a چکیده کاملThis article is an attempt to obtain the numerical solution of functional linear Voltrra two-dimensional integral equations using Radial Basis Function (RBF) interpolation which isbased on linear composition of terms. By using RBF in functional integral equation, rst alinear system C = G will be achieved; then the coecients vector is dened, and nally thetarget function will be approximated. In the end, the validity of the method is shown by anumber of examples. پرونده مقاله -
دسترسی آزاد مقاله
76 - Numerical Solution Two-Dimensional Volterra-Fredholm Integral Equations of the Second Kind with Block-Pulse Functions Based on Legendre Polynomials
Jafar Khazaian Nouredin Parandin Farajollah Mohammadi Yaghoobi Nasrin Karami KabirIn this paper, we present a new numerical technique based on Block-pulse functions to solve two-dimensional Volterra-Fredholm integral equations of the second kind. To produce Block-pulse functions, the orthogonal Legendre polynomials is used. Furthermore, operational m چکیده کاملIn this paper, we present a new numerical technique based on Block-pulse functions to solve two-dimensional Volterra-Fredholm integral equations of the second kind. To produce Block-pulse functions, the orthogonal Legendre polynomials is used. Furthermore, operational matrix is applied to convert two-dimensional Volterra-Fredholm integral equations to a linear algebraic system. The convergence analysis of the new method is discussed. Finally, some numerical examples are given to confirm the applicability and efficiency of the new method for solving two-dimensional Volterra-Fredholm integral equations of the second kind. پرونده مقاله -
دسترسی آزاد مقاله
77 - A Numerical Solution for 2D-Nonlinear Fredholm Integral Equations Based on Hybrid Functions Basis
Maryam Mohammadi A. Zakeri Majid Karami Narges Taheri Raheleh NouraeiThis work considers a numerical method based on the 2D-hybrid block-pulse functions and normalized Bernstein polynomials to solve 2D-nonlinear Fredholm integral equations of the second type. These problems are reduced to a system of nonlinear algebraic equations and sol چکیده کاملThis work considers a numerical method based on the 2D-hybrid block-pulse functions and normalized Bernstein polynomials to solve 2D-nonlinear Fredholm integral equations of the second type. These problems are reduced to a system of nonlinear algebraic equations and solved by Newton's iterative method along with the numerical integration and collocation methods. Also, the convergence theorem for this algorithm is proved. Finally, some numerical examples are given to show the effectiveness and simplicity of the proposed method. پرونده مقاله -
دسترسی آزاد مقاله
78 - DUAL BOUNDARY ELEMENT ANALYSIS OF CRACKED PLATES
A. PortelaThe dual boundary element method is formulated for the analysis of linear elastic cracked plates. The dual boundary integral equations of the method are the displacement and the traction equations. When these equations are simultaneously applied along the crack boundari چکیده کاملThe dual boundary element method is formulated for the analysis of linear elastic cracked plates. The dual boundary integral equations of the method are the displacement and the traction equations. When these equations are simultaneously applied along the crack boundaries, general crack problems can be solved in a single-region formulation, with both crack boundaries discretized with discontinuous boundary elements. The stress intensity factors evaluation is carried out by the J-integral decomposition method which is applied on a circular path, defined around each crack tip. Examples of geometries with edge, and embedded cracks are analyzed. The accuracy and e_ciency of the dual boundary element method and the J-integral make the present formulation ideal for the study of cracked plates. پرونده مقاله -
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79 - ANALYTICAL-NUMERICAL SOLUTION FOR NONLINEAR INTEGRAL EQUATIONS OF HAMMERSTEIN TYPE
J. Rashidinia A. ParsaUsing the mean-value theorem for integrals we tried to solved the nonlinear integral equations of Hammerstein type . The mean approach is to obtain an initial guess with unknown coefficients for unknown function y(x). The procedure of this method is so fast and don't ne چکیده کاملUsing the mean-value theorem for integrals we tried to solved the nonlinear integral equations of Hammerstein type . The mean approach is to obtain an initial guess with unknown coefficients for unknown function y(x). The procedure of this method is so fast and don't need high cpu and complicated programming. The advantages of this method are that we can applied for those integral equations which have not the unique solution too. پرونده مقاله -
دسترسی آزاد مقاله
80 - SPLINE COLLOCATION FOR NONLINEAR FREDHOLM INTEGRAL EQUATIONS
Z. Mahmoodi J. Rashidinia E. BabolianThe collocation method based on cubic B-spline, is developed to approximate the solution of second kind nonlinear Fredholm integral equations. First of all, we collocate the solution by B-spline collocation method then the Newton-Cotes formula use to approximate the int چکیده کاملThe collocation method based on cubic B-spline, is developed to approximate the solution of second kind nonlinear Fredholm integral equations. First of all, we collocate the solution by B-spline collocation method then the Newton-Cotes formula use to approximate the integrand. Convergence analysis has been investigated and proved that the quadrature rule is third order convergent. The presented method is tested with four examples, and the errors in the solution are compared with the existing methods [1, 2, 3, 4] to verify the accuracy and convergent nature of proposed methods. The RMS errors in the solutions are tabulated in table 3 which shows that our method can be applied for large values of n, but the maximum n which has been used by the existing methods are only n = 10, moreover our method is accurate and stable for different values of n. پرونده مقاله -
دسترسی آزاد مقاله
81 - NUMERICAL APPROACH TO SOLVE SINGULAR INTEGRAL EQUATIONS USING BPFS AND TAYLOR SERIES EXPANSION
Ahmad Shahsavaran Akbar Shahsavaran Forough FotrosIn this paper, we give a numerical approach for approximating the solution of second kind Volterra integral equation with Logarithmic kernel using Block Pulse Functions (BPFs) and Taylor series expansion. Also, error analysis shows efficiency and applicability of the چکیده کاملIn this paper, we give a numerical approach for approximating the solution of second kind Volterra integral equation with Logarithmic kernel using Block Pulse Functions (BPFs) and Taylor series expansion. Also, error analysis shows efficiency and applicability of the presented method. Finally, some numerical examples with exact solution are given. پرونده مقاله -
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82 - A HOMOTOPY PERTURBATION ALGORITHM AND TAYLOR SERIES EXPANSION METHOD TO SOLVE A SYSTEM OF SECOND KIND FREDHOLM INTEGRAL EQUATIONS
S. M. MirzaeiIn this paper, we will compare a Homotopy perturbation algorithm and Taylor series expansin method for a system of second kind Fredholm integral equations. An application of He’s homotopy perturbation method is applied to solve the system of Fredholm integral equa چکیده کاملIn this paper, we will compare a Homotopy perturbation algorithm and Taylor series expansin method for a system of second kind Fredholm integral equations. An application of He’s homotopy perturbation method is applied to solve the system of Fredholm integral equations. Taylor series expansin method reduce the system of integral equations to a linear system of ordinary differential equation. پرونده مقاله -
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83 - NUMERICAL SOLUTION OF DELAY INTEGRAL EQUATIONS BY USING BLOCK PULSE FUNCTIONS ARISES IN BIOLOGICAL SCIENCES
M. Nouri K. MaleknejadThis article proposes a direct method for solving three types of integral equations with time delay. By using operational matrix of integration, integral equations can be reduced to a linear lower triangular system which can be directly solved by forward substitution. N چکیده کاملThis article proposes a direct method for solving three types of integral equations with time delay. By using operational matrix of integration, integral equations can be reduced to a linear lower triangular system which can be directly solved by forward substitution. Numerical examples shows that the proposed scheme have a suitable degree of accuracy. پرونده مقاله -
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84 - HYBRID FUNCTIONS APPROACH AND PIECEWISE CONSTANT FUNCTION BY COLLOCATION METHOD FOR THE NONLINEAR VOLTERRA-FREDHOLM INTEGRAL EQUATIONS
S. M. MirzaeiIn this work, we will compare two approximation method based on hybrid Legendre andBlock-Pulse functions and a computational method for solving nonlinear Fredholm-Volterraintegral equations of the second kind which is based on replacement of the unknown functionby trunc چکیده کاملIn this work, we will compare two approximation method based on hybrid Legendre andBlock-Pulse functions and a computational method for solving nonlinear Fredholm-Volterraintegral equations of the second kind which is based on replacement of the unknown functionby truncated series of well known Block-Pulse functions (BPfs) expansion پرونده مقاله -
دسترسی آزاد مقاله
85 - APPROXIMATION SOLUTION OF TWO-DIMENSIONAL LINEAR STOCHASTIC FREDHOLM INTEGRAL EQUATION BY APPLYING THE HAAR WAVELET
Morteza Khodabin Khosrow Maleknejad Mohsen FallahpourIn this paper, we introduce anefficient method based on Haar wavelet to approximate a solutionfor the two-dimensional linear stochastic Fredholm integralequation. We also give an example to demonstrate the accuracy ofthe method.In this paper, we introduce anefficient method based on Haar wavelet to approximate a solutionfor the two-dimensional linear stochastic Fredholm integralequation. We also give an example to demonstrate the accuracy ofthe method. پرونده مقاله -
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86 - CAS WAVELET METHOD FOR THE NUMERICAL SOLUTION OF BOUNDARY INTEGRAL EQUATIONS WITH LOGARITHMIC SINGULAR KERNELS
Hojatollah Adibi M. Shamooshaky Pouria AssarIn this paper, we present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the Laplacian equation. Themethod is based on the use of the Galerkin method with CA چکیده کاملIn this paper, we present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the Laplacian equation. Themethod is based on the use of the Galerkin method with CAS wavelets constructed on the unit interval as basis.This approach utilizes the non-uniform Gauss-Legendre quadrature rule for approximating logarithm-like singularintegrals and so reduces the solution of boundary integral equations to the solution of linear systems of algebraicequations. The properties of CAS wavelets are used to make the wavelet coe±cient matrices sparse, which eventuallyleads to the sparsity of the coe±cient matrix of the obtained system. Finally, the validity and e±ciency of the newtechnique are demonstrated through a numerical example. پرونده مقاله -
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87 - Fixed Point Theorems in Orthogonal Intuitionistic Fuzzy b-metric Spaces with an Application to Fredholm Integral Equation
Fahim Ud Din Muhammad Saeed Khaleel Ahmad Umar Ishtiaq Salvatore SessaIn this manuscript, the concept of an orthogonal intuitionistic fuzzy b-metric space is initiated as a generalization of an intuitionistic fuzzy b-metric space. We presented some fixed point results in this setting. For the validity of the obtained results, some non-tri چکیده کاملIn this manuscript, the concept of an orthogonal intuitionistic fuzzy b-metric space is initiated as a generalization of an intuitionistic fuzzy b-metric space. We presented some fixed point results in this setting. For the validity of the obtained results, some non-trivial examples are given. In the last part, we established an application on the existence of a unique solution of a Fredholm-type integral equation. پرونده مقاله
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