Volterra integral equation

دسترسی آزاد مقاله

1 - حل عددی معادلات انتگرال جبری ولترا با روش بسط تیلور
عزیزاله باباخانی الهام انتقامی حسن حسین زاده

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 چکیده کامل

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.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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2 - کاربرد روش تابع هسته برای حل یک کلاس از معادلات انتگرال خطی دو بعدی با هسته منفرد ضعیف
محمد رضا اصلاحچی مریم رضایی

در 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 کامل

در 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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3 - حل معادله انتگرال ولترای نوع دوم خطی یک بعدی در فضای هسته بازتولید
عباس فضلی شهنام جوادی

در 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 کامل

در 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

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4 - روش مش لس برای مسئله کنترل بهینه معادلات انتگرال ولترا با استفاده از توابع پایه شعاعی چند درجه دو
ژینوس نظری مله هما الماسیه

در 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 کامل

در 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

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5 - A solution for Volterra Integral Equations of the First Kind Based on Bernstein Polynomials
M. Mohamadi E. Babolian S. Yousefi

In 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 کامل

In 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

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6 - A Fast and Accurate Expansion-Iterative Method for Solving Second Kind Volterra Integral Equations
S. Hatamzadeh-Varmazyar Z. Masouri

This 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 کامل

This 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

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7 - The Use of Fuzzy Variational Iteration Method For Solving Second-Order Fuzzy Abel-Volterra Integro-Differential Equations‎
S. Sadigh Behzadi

In 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 کامل

In 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

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8 - Solution of Nonlinear Fredholm-Volterra Integral Equations via Block-Pulse ‎Functions
F. Abbasi M. Mohamadi

In 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 کامل

In 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

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9 - Solving Volterra Integral Equations of the Second Kind with Convolution ‎Kernel‎
M. S. Barikbin A. R. Vahidi T. ِDamercheli

In 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 &lrm;et al., &lrm;&lrm;[K. Maleknejad &lrm;and Aghazadeh, Numerical solution of Volterr چکیده کامل

In 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 &lrm;et al., &lrm;&lrm;[K. Maleknejad &lrm;and Aghazadeh, Numerical solution of Volterra integral equations of the second kind with convolution kernel by using Taylor-series expansion method, &lrm;Appl. Math. Comput.&lrm; (2005)]&lrm; to gain the approximate solution of the second kind Volterra integral equations with convolution kernel and Maleknejad &lrm;et al. &lrm;[K. Maleknejad &lrm;and&lrm; T. Damercheli, Improving the accuracy of solutions of the linear second kind volterra integral equations system by using the Taylor expansion method, &lrm;Indian J. Pure Appl. Math.&lrm; (2014)] &lrm;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 &lrm;stable.&lrm; پرونده مقاله

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10 - On the Modified Block-Pulse Function for Volterra Integral Equation of The First ‎Kind‎
M. Mohammadi A. R. Vahidi T. Damercheli S. Khezerloo M. Nouri

10.30495/ijim.2022.20272

In 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 کامل

In 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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11 - A New Efficient Method for Solving System of Fuzzy Volterra Integral Equations Based on Fibonacci ‎Polynomials
T. Sheverini M. Paripour N. Karamikabir

10.30495/ijim.2022.19394

Here, 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 کامل

Here, 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

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12 - A Hybrid Approach for Systems of Integral ‎Equations‎
J. Biazar Y. Parvari Moghaddam kh. Sadri

10.30495/ijim.2023.21178

&lrm;In this paper&lrm;, &lrm;we present a computational method for solving systems of Volterra and Fredholm integral equations which is a hybrid approach&lrm;, &lrm;based on the third-order Chebyshev polynomials and block-pulse functions which we will refer to as (HBV) چکیده کامل

&lrm;In this paper&lrm;, &lrm;we present a computational method for solving systems of Volterra and Fredholm integral equations which is a hybrid approach&lrm;, &lrm;based on the third-order Chebyshev polynomials and block-pulse functions which we will refer to as (HBV)&lrm;, &lrm;for short&lrm;. &lrm;The existence and uniqueness of the solutions are addressed&lrm;. &lrm;Some examples are provided to clarify the efficiency and accuracy of the method&lrm;. پرونده مقاله

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13 - A New Approach for Solving Volterra Integral Equations Using The Reproducing Kernel ‎Method
R. Ketabchi&lrm; R. Mokhtari E. Babolian

This 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 کامل

This 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 &lrm;examples. پرونده مقاله

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14 - Numerical solution of the system of Volterra integral equations of the first kind
A. Armand Z. Gouyandeh

This 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 کامل

This 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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15 - Spectral Scheme for Solving Fuzzy Volterra Integral Equations of First Kind
Laleh Hooshangian

This 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 کامل

This 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

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16 - Spectral method for Solving Fuzzy Volterra Integral Equations of Second kind
Laleh Hooshangian

This 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 کامل

This 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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17 - A novel method to solve fuzzy Volterra integral equations using collocation method
Nouredin Parandin Mohsen Darabi

Fuzzy 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 کامل

Fuzzy 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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18 - Spectral Method for Solving Fuzzy Volterra Integral Equations of Second kind
Laleh Hooshangian

This 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 کامل

This 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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19 - Evaluating the solution for second kind nonlinear Volterra Fredholm integral equations using hybrid method
Ahamd Shahsavaran Akbar Shahsavaran

In 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 کامل

In 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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20 - Numerical Solution of a New Type Fuzzy Nonlinear Volterra Integral Equations
Laleh Hooshangian

Fuzzy 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 کامل

Fuzzy 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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21 - Numerical solution of Hammerstein Fredholm and Volterra integral equations of the second kind using block pulse functions and collocation method
M. M. Shamivand A. Shahsavaran

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.

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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22 - 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-Jazi

This 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 کامل

This 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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23 - Evaluating the solution for second kind nonlinear Volterra Fredholm integral equations using hybrid method
Ahmad Shahsavaran Akbar Shahsavaran

In 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 کامل

In 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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24 - Numerical solution of Fredholm and Volterra integral equations using the normalized Müntz−Legendre polynomials
فرشته صائمی حمیده ابراهیمی محمود شفیعی

The 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 کامل

The 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

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25 - Numerical solution of a type of weakly singular nonlinear Volterra integral equation by Tau Method
H. Laeli Dastjerdi M. Nili Ahmadabadi

&lrm;In this paper&lrm;, &lrm;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&lrm;. &lrm;In this method&lrm;, &lrm;a tran چکیده کامل

&lrm;In this paper&lrm;, &lrm;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&lrm;. &lrm;In this method&lrm;, &lrm;a transformation of the independent variable is first introduced in order to obtain a new equation with smoother solution&lrm;. &lrm;Error analysis of this method is also presented&lrm;. &lrm;Some numerical examples are provided to illustrate the accuracy and computational efficiency of the method&lrm;. پرونده مقاله

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26 - Hyers–Ulam–Rassias stability of impulsive Volterra integral equation via a fixed point approach
R. Shah A. Zada

&lrm;In this paper&lrm;, &lrm;we establish the Hyers--Ulam--Rassias stability and the Hyers--Ulam stability of impulsive Volterra integral equation by using a fixed point method&lrm;.

&lrm;In this paper&lrm;, &lrm;we establish the Hyers--Ulam--Rassias stability and the Hyers--Ulam stability of impulsive Volterra integral equation by using a fixed point method&lrm;. پرونده مقاله

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27 - Approximate Solution of the Second Order Initial Value Problem by Using Epsilon Modified Block-Pulse Function
Mahnaz Mohammadi Alireza Vahidi Saeid Khezerloo

The 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 کامل

The 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

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28 - NUMERICAL APPROACH TO SOLVE SINGULAR INTEGRAL EQUATIONS USING BPFS AND TAYLOR SERIES EXPANSION
Ahmad Shahsavaran Akbar Shahsavaran Forough Fotros

In 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 کامل

In 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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