فهرست مقالات Operational ‎matrix‎

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  1 - An Effective Computational Approach by Hybrid Functions Operational Matrix for Solving Mixed Kind of the Partial Integro-Differential Equations
  یاسر رستمی
  In the present paper, a new method is introduced for the approximate solution of two-dimensional mixed Volterra-Fredholm Partial integro-differential equations with initial conditions using twodimensional hybrid Bernstein polynomials and Block-Pulse functions. For this چکیده کامل

  In the present paper, a new method is introduced for the approximate solution of two-dimensional mixed Volterra-Fredholm Partial integro-differential equations with initial conditions using twodimensional hybrid Bernstein polynomials and Block-Pulse functions. For this purpose, an operational matrix of product and integration of the cross-product and differentiation are introduced that essentially of hybrid functions. The use of these operational matrices simplifies considerably the structure of the computational used for a set of algebraic equations methods for the solution of partial integro-differential equations.. The use of these operational matrices simplifies considerably the structure of the computational used for a set of algebraic equations methods for the solution of partial integro-differential equations.. The use of these operational matrices simplifies considerably the structure of the computational used for a set of algebraic equations methods for the solution of partial integro-differential equations. Convergence analysis and some numerical results are presented to illustrate the effectiveness and accuracy of the method. پرونده مقاله
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  2 - حل عددی معادلات دیفرانسیل معمولی منفرد غیرخطی حاصل شده دربیولوژی، ازطریق ماتریس عملیاتی چند جمله ای های زرنیکه شعاعی
  محمد علی عبادی الهام السادات هاشمی زاده امیرحسین رفاهی شیخانی
  هدف از این مقاله، ارائه رویکردی عددی جدید، برای حل معادلات دیفرانسیل منفرد غیر خطی که در زمینه ی بیولوژی حاصل می شوند، می باشد. این قبیل معادلات در مسائل متعدد بیولوژی نظیر انتشار اکسیژن در سلول های خونی، انتشار گرما از سر انسان و رشد تومورهای سرطانی ظاهر می شوند. در ای چکیده کامل

  هدف از این مقاله، ارائه رویکردی عددی جدید، برای حل معادلات دیفرانسیل منفرد غیر خطی که در زمینه ی بیولوژی حاصل می شوند، می باشد. این قبیل معادلات در مسائل متعدد بیولوژی نظیر انتشار اکسیژن در سلول های خونی، انتشار گرما از سر انسان و رشد تومورهای سرطانی ظاهر می شوند. در این مقاله این معادلات به کمک یک روش عددی جدید بر پایه چند جمله های زرنیکه شعاعی حل می‌شوند. در روش ارائه شده برای اولین بار ماتریس های عملیاتی مشتق گیری این توابع به دست آمده و سپس بر اساس ماتریس های عملیاتی برای مشتق توابع زرنیکه شعاعی، معادله ی دیفرانسیل اصلی به یک دستگاه از معادلات غیر خطی جبری تبدیل شود که به راحتی حل پذیرند. پیاده سازی این روش ساده و جذاب است. در پایان، مثال های کاربردی برای نشان دادن پیاده سازی روش ارائه شده و مقایسه جوابهای به دست آمده از این روش با جواب های سایر روش های معروف ارائه و حل شده است، و نتایج حاصل از آن، حاکی از دقت و کارایی این روش عددی است. پرونده مقاله
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  3 - ارائه دو مدل برای تحلیل عددی جواب معادلات دیفرانسیل-انتگرال کسری و مقایسه آنها
  محمود بهروزی فر
  در این مقاله، دو مدل برای تحلیل عددی جواب معادلات دیفرانسیل-انتگرال کسری ارائه می دهیم و سپس به مقایسه نتایج بکارگیری آنها بر روی مسائل متنوع می پردازیم. برای این منظور ابتدا ماتریس‌های عملیاتی چند جمله‌ای‌های ژاکوبی را بیان کرده و سپس هر مسئله را با دو روش حل می‌نماییم چکیده کامل

  در این مقاله، دو مدل برای تحلیل عددی جواب معادلات دیفرانسیل-انتگرال کسری ارائه می دهیم و سپس به مقایسه نتایج بکارگیری آنها بر روی مسائل متنوع می پردازیم. برای این منظور ابتدا ماتریس‌های عملیاتی چند جمله‌ای‌های ژاکوبی را بیان کرده و سپس هر مسئله را با دو روش حل می‌نماییم: روش ماتریس عملیاتی مشتق مرتبه کسری کاپوتو و روش ماتریس عملیاتی انتگرال مرتبه کسری ریمان-لیوویل. در هر دو روش با استفاده از تکنیک نقطه گذاری به یک دستگاه معادلات جبری خطی یا غیرخطی خواهیم رسید با کمک روش تکراری نیوتن حل می شوند. روش‌های ارائه شده روی چند مثال پیاده سازی شده است و نتایج عددی حاصل بیانگر کارایی بالای هر دو روش است. لازم به ذکر است که تمامی محاسبات با کمک نرم افزار متمتیکا انجام شده است. نتایج عددی نشان می‌دهد که برای معادله دیفرانسیلی که جواب آن بصورت چند جمله ای می باشد بهتر است از روش اول و در معادله غیر خطی که جواب آن بصورت تابع متعالی است بهتر است که روش دوم استفاده شود. پرونده مقاله
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  4 - حل عددی مدل کسری عفونت HIV در سلولهای CD4+T
  محمد رضا دوستدار طیبه دمرچلی علیرضا وحیدی
  در این مقاله، مدل کسری عفونت HIV در سلولهای CD4+T بررسی قرار میگیرد. در این مدل، مشتقات کسری در مفهوم کاپوتو در نظر گرفته میشوند. در این روش، دستگاه معادلات دیفرانسیل معمولی از مرتبه کسری به یک دستگاه معادلات جبری تبدیل میگردد که میتوان آن را با استفاده از یک روش عددی م چکیده کامل

  در این مقاله، مدل کسری عفونت HIV در سلولهای CD4+T بررسی قرار میگیرد. در این مدل، مشتقات کسری در مفهوم کاپوتو در نظر گرفته میشوند. در این روش، دستگاه معادلات دیفرانسیل معمولی از مرتبه کسری به یک دستگاه معادلات جبری تبدیل میگردد که میتوان آن را با استفاده از یک روش عددی مناسب حل نمود. همچنین، در بحث آنالیز خطا، کران بالای خطا ارائه شده است. کارایی و دقت روش، با استفاده از یک نمونه عددی برای برخی مشتقات صحیح و کسری بررسی و برخی مقایسه ها و نتایج گزارش شده است. در این مقاله، مدل کسری عفونت HIV در سلولهای CD4+T بررسی قرار میگیرد. در این مدل، مشتقات کسری در مفهوم کاپوتو در نظر گرفته میشوند. در این روش، دستگاه معادلات دیفرانسیل معمولی از مرتبه کسری به یک دستگاه معادلات جبری تبدیل میگردد که میتوان آن را با استفاده از یک روش عددی مناسب حل نمود. همچنین، در بحث آنالیز خطا، کران بالای خطا ارائه شده است. کارایی و دقت روش، با استفاده از یک نمونه عددی برای برخی مشتقات صحیح و کسری بررسی و برخی مقایسه ها و نتایج گزارش شده است. پرونده مقاله
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  5 - ماتریس عملیاتی جدید برای حل یک کلاس از مسائل کنترل بهینه با مشتق کسری ریمان- لیوویل اصلاح شده جمیره
  محسن علی پور پریسا الله‌قلی
  در این مقاله، ما روش طیفی را برمبنای چندجمله­ای­های برنشتاین برای حل یک کلاس از مسائل کنترل بهینه با مشتق کسری ریمانلیوویل اصلاح شده جمیره به کار می­بریم. در مرحله اول، پایه دوگان و ماتریس عملیاتی حاصلضرب را براساس پایه برنشتاین معرفی می­نمائیم. سپس ماتر چکیده کامل

  در این مقاله، ما روش طیفی را برمبنای چندجمله­ای­های برنشتاین برای حل یک کلاس از مسائل کنترل بهینه با مشتق کسری ریمانلیوویل اصلاح شده جمیره به کار می­بریم. در مرحله اول، پایه دوگان و ماتریس عملیاتی حاصلضرب را براساس پایه برنشتاین معرفی می­نمائیم. سپس ماتریس عملیاتی برنشتاین را برای مشتقات کسری ریمانلیوویل اصلاح شده جمیره بدست می­آوریم که تا کنون انجام نشده است. با استفاده از تقریب توابع براساس پایه برنشاین و ماتریس­های عملیاتی ذکر شده، مسئله کنترل بهینه با مشتق کسری ریمانلیوویل اصلاح شده جمیره به یک سیستم معادلات جبری کاهش می­یابد که با استفاده از روش تکراری نیوتن به سادگی قابل حل می­باشد. روش مطرح شده را برای حل دو مسئله بکار می­گیریم. نتایج عددی نشان می­دهد که جواب­های تقریبی حاصل، از دقت بالایی برخوردار هستند. برخی مقایسه­ها با روش دیگر تضمین می­کند که نتایج منطقی می­باشند. همچنین همانطور که انتظار می­رفت، وقتی مرتبه مشتق کسری به عدد 1 میل نماید، جواب­های بدست آمده به جواب­های کلاسیک میل می­نماید. پرونده مقاله
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  6 - حل عددی مسائل اشتورم-لیوویل با توابع کاردینال چبیشف
  محمد شهریاری بهزاد نعمتی سرای فیروز پاشائی
  در این مقاله، هدف اصلی ارائه‌ی یک روش عددی نوین برای تقریب مقادیر ویژه و توابع ویژه‌ی در حل مسأله‌ی اشتورم-لیوویل منظم است. به عنوان یک هدف راهبردی، ساختار توابع کاردینال چبیشف مبتنی بر چندجمله­ای­های چبیشف نوع اول بیان و بررسی می­شود. شیوه‌ی محوری کار، تقلی چکیده کامل

  در این مقاله، هدف اصلی ارائه‌ی یک روش عددی نوین برای تقریب مقادیر ویژه و توابع ویژه‌ی در حل مسأله‌ی اشتورم-لیوویل منظم است. به عنوان یک هدف راهبردی، ساختار توابع کاردینال چبیشف مبتنی بر چندجمله­ای­های چبیشف نوع اول بیان و بررسی می­شود. شیوه‌ی محوری کار، تقلیل مسأله‌ی اشتورم-لیوویل به یک دستگاه معادلات جبری است که نیازمند به کارگیری ماتریس عملیاتی مشتق خواهد بود. حل دستگاه معادلات جبری منجر به تقریب عددی مقادیر ویژه و توابع ویژه مسأله اصلی می­گردد. ارائه‌ی مثال‌های عددی عملکرد روش و اهمیت آن را نمایان‌تر می‌سازد. پرونده مقاله
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  7 - A Survey of Direct Methods for Solving Variational Problems
  Maryam Gholami Mohammad Norouzi
  This study presents a comparative survey of direct methods for solving Variational Problems. Thisproblems can be used to solve various differential equations in physics and chemistry like RateEquation for a chemical reaction. There are procedures that any type of a diff چکیده کامل

  This study presents a comparative survey of direct methods for solving Variational Problems. Thisproblems can be used to solve various differential equations in physics and chemistry like RateEquation for a chemical reaction. There are procedures that any type of a differential equation isconvertible to a variational problem. Therefore finding the solution of a differential equation isequivalent to solving its related variational problem. The objective of this paper is to describe themajor direct methods that have been developed over the years for solving these types of problems. Inthis paper we focus on using orthogonal polynomials and triangular functions as basis functions. Eachmethod needs computing operational matrices and some other parameters which are presented aswell. Several numerical examples are then included to demonstrate the accuracy and applicability ofthe reviewed methods. Computational concerns are then discussed to provide a guideline to thepreferred and the most accurate method. پرونده مقاله
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  8 - An Efficient Numerical Algorithm For Solving Linear Differential Equations of Arbitrary Order And Coefficients
  S. Hatamzadeh-Varmazyar Z. Masouri
  Referring to one of the recent works of the authors, presented in~\cite{differentialbpf}, for numerical solution of linear differential equations, an alternative scheme is proposed in this article to considerably improve the accuracy and efficiency. For this purpose, tr چکیده کامل

  Referring to one of the recent works of the authors, presented in~\cite{differentialbpf}, for numerical solution of linear differential equations, an alternative scheme is proposed in this article to considerably improve the accuracy and efficiency. For this purpose, triangular functions as a set of orthogonal functions are used. By using a special representation of the vector forms of triangular functions and the related operational matrix of integration, solving the differential equation reduces to solve a linear system of algebraic equations. The formulation of the method is quite general, such that any arbitrary linear differential equation may be solved by it. Moreover, the algorithm does not include any integration and, instead, uses just sampling of functions, that results in a lower computational complexity. Also, the formulation of this approach needs no modification when a singularity occurs in the coefficients of differential equation. Some problems are numerically solved by the proposed method to illustrate that it is much more accurate and applicable than the prior method in~\cite{differentialbpf}. پرونده مقاله
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  9 - 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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  10 - Solving the First-Order Linear Matrix Differential Equations Using Bernstein Matrix Approach
  Z. Lorkojouri N. Mikaeilvand E. Babolian
  This paper uses a new framework for solving a class of linear matrix differential equations. For doing so, the operational matrix of the derivative based on the shifted Bernstein polynomials together with the collocation method are exploited to decrease the principal pr چکیده کامل

  This paper uses a new framework for solving a class of linear matrix differential equations. For doing so, the operational matrix of the derivative based on the shifted Bernstein polynomials together with the collocation method are exploited to decrease the principal problem to system of linear matrix equations. An error estimation of this method is provided. Numerical experiments are reported to show the applicably and efficiency of the propounded method. پرونده مقاله
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  11 - A Numerical Method For Solving Physiology Problems By Shifted Chebyshev Operational Matrix
  E. Hashemizadeh F. Mahmoodi
  In this study, a numerical solution of singular nonlinear differential equations, stemming from biology and physiology problems, is proposed. The methodology is based on the shifted Chebyshev polynomials operational matrix of derivative and collocation. To assess the ac چکیده کامل

  In this study, a numerical solution of singular nonlinear differential equations, stemming from biology and physiology problems, is proposed. The methodology is based on the shifted Chebyshev polynomials operational matrix of derivative and collocation. To assess the accuracy of the method, five numerical problems, such as the human head, Oxygen diffusion and Bessel differential equation, were solved. The numerical results were compared with other existed methods in tables for verification. پرونده مقاله
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  12 - Application of Laguerre Polynomials for Solving Infinite Boundary Integro-Differential Equations
  A. Riahifar M. Matinfar
  In this study‎, ‎an efficient method is presented for solving infinite boundary integro-differential equations (IBI-DE) of the second kind with degenerate kernel in terms of Laguerre polynomials‎. ‎Properties of these polynomials and operational matrix o چکیده کامل

  In this study‎, ‎an efficient method is presented for solving infinite boundary integro-differential equations (IBI-DE) of the second kind with degenerate kernel in terms of Laguerre polynomials‎. ‎Properties of these polynomials and operational matrix of integration are first presented‎. ‎These properties are then used to transform the integral equation to a matrix equation which corresponds to a linear system of algebraic equations with unknown Laguerre coefficients‎. ‎We prove the convergence analysis of method applied to the solution integro-differential equations‎. ‎Finally‎, ‎numerical examples illustrate the efficiency and accuracy of the method. پرونده مقاله
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  13 - Bernstein ‎M‎ulti-Scaling Operational Matrix Method for Nonlinear Matrix Differential Models of Second-‎Order‎
  M. Mohamadi E. Babolian S. A. Yousefi
  In The current paper presents an idea for solving a class of linear matrix differential equations of second order. To perform so, the operational matrix of the integration based on the Bernstein multi-scaling polynomials are used to reduce the main problem to system of چکیده کامل

  In The current paper presents an idea for solving a class of linear matrix differential equations of second order. To perform so, the operational matrix of the integration based on the Bernstein multi-scaling polynomials are used to reduce the main problem to system of matrix equations. Numerical experiments illustrate the applicably and efficiency of the propounded ‎technique.‎ پرونده مقاله
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  14 - Using New Operational Matrix for Solving Nonlinear Fractional Integral Equations
  F. Saleki R. ٍٍEzzati
  In 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 کامل

  In 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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  15 - 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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  16 - A Novel Shifted Jacobi Operational Matrix for Solution of Nonlinear Fractional Variable-Order Differential Equation with Proportional ‎Delays‎
  H. R. Khodabandelo E. Shivanian S. Abbasbandy
  10.30495/ijim.2022.64043.1555
  This work presents the generalized nonlinear multi-terms fractional variable-order differential equation with proportional delays. In this paper, a novel shifted Jacobi operational matrix technique is introduced to solve a class of these equations mentioned, so that the چکیده کامل

  This work presents the generalized nonlinear multi-terms fractional variable-order differential equation with proportional delays. In this paper, a novel shifted Jacobi operational matrix technique is introduced to solve a class of these equations mentioned, so that the main problem becomes a system of algebraic equations that we can solve numerically. The suggested technique is successfully developed for the aforementioned problem. Comprehensive numerical tests are provided to demonstrate the generality, efficiency, accuracy of presented scheme and the flexibility of this technique. The numerical experiments compared it with other existing methods such as Reproducing Kernel Hilbert Space method ($ RKHSM $). Comparing the results of these methods as well as comparing the current method ($NSJOM$) with the true solution, indicating the validity and efficiency of this scheme. Note that the procedure is easy to implement and this technique will be considered as a generalization of many numerical schemes. Furthermore, the error and its bound are estimated. پرونده مقاله
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  17 - Bernoulli operational matrix method for system of linear Volterra integral ‎equations
  E. Hashemizadeh‎ M. Mohsenyzadeh
  In this paper, the numerical technique based on hybrid Bernoulli and Block-Pulse functions has been developed to approximate the solution of system of linear Volterra integral equations. System of Volterra integral equations arose in many physical problems such as elast چکیده کامل

  In this paper, the numerical technique based on hybrid Bernoulli and Block-Pulse functions has been developed to approximate the solution of system of linear Volterra integral equations. System of Volterra integral equations arose in many physical problems such as elastodynamic, quasi-static visco-elasticity and magneto-electro-elastic dynamic problems. These functions are formed by the hybridization of Bernoulli polynomials and Block-Pulse functions which are orthonormal and have compact support on $[0, 1]$. By these orthonormal bases we drove new operational matrix which was a sparse matrix. By use of this new operational matrix we reduces the system of integral equations to a system of linear algebraic equations that can be solved easily by any usual numerical method. The numerical results obtained by the presented method have been compared with some existed methods and they have been in good agreement with the analytical solutions and other methods that prove the profit and efficiency of the proposed ‎method.‎ پرونده مقاله
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  18 - Numerical Solution of Fredholm Integro-differential Equations By Using Hybrid Function Operational Matrix of ‎Differentiation‎
  R. Jafri R. Ezzati K. ‎Maleknejad‎
  In this paper‎, ‎first‎, ‎a numerical method is presented for solving a class of linear Fredholm integro-differential equation‎. ‎The operational matrix of derivative is obtained by introducing hybrid third kind Chebyshev polynomials and Block-pu چکیده کامل

  In this paper‎, ‎first‎, ‎a numerical method is presented for solving a class of linear Fredholm integro-differential equation‎. ‎The operational matrix of derivative is obtained by introducing hybrid third kind Chebyshev polynomials and Block-pulse functions‎. ‎The application of the proposed operational matrix with tau method is then utilized to transform the integro-differential equations to the algebraic equations‎. ‎Finally‎, ‎show the efficiency of the proposed method is indicated by some numerical ‎examples.‎ پرونده مقاله
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  19 - Approximation solution of two-dimensional linear stochastic Volterra-Fredholm integral equation via two-dimensional Block-pulse ‎functions
  M. Fallahpour‎‎ M. Khodabin‎ K. Maleknejad‎
  In 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 کامل

  In 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
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  20 - Numerical solution of nonlinear integral equations by Galerkin methods with hybrid Legendre and Block-Pulse functions
  M. Tavassoli Kajani S. Mahdavi
  In 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 کامل

  In 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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  21 - Numerical Solution of Multidimensional Exponential Levy Equation by Block Pulse Function
  Minoo Bakhshmohammadlou Rahman Farnoosh
  10.22034/amfa.2020.1873599.1260
  The multidimensional exponential Levy equations are used to describe many stochastic phenomena such as market fluctuations. Unfortunately in practice an exact solution does not exist for these equations. This motivates us to propose a numerical solution for n-dimensiona چکیده کامل

  The multidimensional exponential Levy equations are used to describe many stochastic phenomena such as market fluctuations. Unfortunately in practice an exact solution does not exist for these equations. This motivates us to propose a numerical solution for n-dimensional exponential Levy equations by block pulse functions. We compute the jump integral of each block pulse function and present a Poisson operational matrix. Then we reduce our equation to a linear lower triangular system by constant, Wiener and Poisson operational matrices. Finally using the forward substitution method, we obtain an approximate answer with the convergence rate of O(h). Moreover, we illustrate the accuracy of the proposed method with a 95% confidence interval by some numerical examples.‎ پرونده مقاله
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  22 - Application of optimization algorithm to nonlinear fractional optimal control problems
  Asma Moradikashkooli Hamid Haj Seyyed Javadi Sam Jabbehdari
  10.22094/jcr.2023.1996770.1317
  In this study, an optimization algorithm based on the generalized Laguerre polynomials (GLPs) as the basis functions and the Lagrange multipliers is presented to obtain approximate solution of nonlinear fractional optimal control problems. The Caputo fractional derivati چکیده کامل

  In this study, an optimization algorithm based on the generalized Laguerre polynomials (GLPs) as the basis functions and the Lagrange multipliers is presented to obtain approximate solution of nonlinear fractional optimal control problems. The Caputo fractional derivatives of GLPs is constructed. The operational matrices of the Caputo and ordinary derivatives are introduced. The established scheme transforms obtaining the solution of such problems into finding the solution of algebraic systems of equations by approximating the state and control variables using the mentioned basis functions. The method is very accurate and is computationally very attractive. Examples are included to provide the capacity of the proposal method. پرونده مقاله
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  23 - An efficient technique for solving systems of integral equations
  حمیده ابراهیمی
  In 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 کامل

  In 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
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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 - Legendre Wavelet Method for a Class of Fourth-Order Boundary Value Problems
  سرکوت عبدی آرام عزیزی محمود شفیعی جمشید سعیدیان
  In this paper we apply an approximate method based on Galerkin approach with Legendre wavelets basis, on a class of fourth order boundary value problems. The approach reduces the main equation to a system of linear algebraic equations that could be solved numerically. T چکیده کامل

  In this paper we apply an approximate method based on Galerkin approach with Legendre wavelets basis, on a class of fourth order boundary value problems. The approach reduces the main equation to a system of linear algebraic equations that could be solved numerically. The operational matrix of the method is obtained, and the convergence of the method is proved. we approximate the solution and its higher order derivatives, for some special examples and compare the results with some other numerical methods. The results show the effectiveness of the proposed method. پرونده مقاله
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  26 - Application of triangular functions for solving the vasicek model
  Z. Sadati Kh. Maleknejad
  This paper introduces a numerical method for solving the vasicek model by using a stochastic operational matrix based on the triangular functions (TFs) in combination with the collocation method. The method is stated by using conversion the vasicek model to a stochastic چکیده کامل

  This paper introduces a numerical method for solving the vasicek model by using a stochastic operational matrix based on the triangular functions (TFs) in combination with the collocation method. The method is stated by using conversion the vasicek model to a stochastic nonlinear system of $2m+2$ equations and$2m+2$ unknowns. Finally, the error analysis and some numerical examples are providedto demonstrate applicability and accuracy ofthis method. پرونده مقاله
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  27 - A Chebyshev functions method for solving linear and nonlinear fractional differential equations based on Hilfer fractional derivative
  M. H. Derakhshan A. Aminataei
  The theory of derivatives and integrals of fractional in fractional calculus have found enormousapplications in mathematics, physics and engineering so for that reason we needan efficient and accurate computational method for the solution of fractional differential equa چکیده کامل

  The theory of derivatives and integrals of fractional in fractional calculus have found enormousapplications in mathematics, physics and engineering so for that reason we needan efficient and accurate computational method for the solution of fractional differential equations.This paper presents a numerical method for solving a class of linear and nonlinear multi-order fractional differential equations with constant coefficients subject to initial conditions based on the fractional order Chebyshev functions that this function is defined as follows:\begin{equation*}\overline{T}_{i+1}^{\alpha}(x)=(4x^{\alpha}-2)\overline{T}_{i}^{\alpha}(x)\overline{T}_{i-1}^{\alpha}(x),\,i=0,1,2,\ldots,\end{equation*}where $\overline{T}_{i+1}^{\alpha}(x)$ can be defined by introducing the change of variable $x^{\alpha},\,\alpha>0$, on the shifted Chebyshevpolynomials of the first kind. This new method is an adaptation of collocationmethod in terms of truncated fractional order Chebyshev Series. To do this method, a new operational matrix of fractional order differential in the Hilfer sense for the fractional order Chebyshev functions is derived. By using this method we reduces such problems to those ofsolving a system of algebraic equations thus greatly simplifying the problem. At the end of this paper, several numerical experiments are given to demonstrate the efficiency and accuracy of the proposed method. پرونده مقاله
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  28 - 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 Kabir
  10.30495/ijm2c.2022.688969
  In 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 کامل

  In 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
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  29 - NUMERICAL SOLUTION OF INTEGRO-DIFFERENTIAL EQUATION BY USING CHEBYSHEV WAVELET OPERATIONAL MATRIX OF INTEGRATION
  M. A. Fariborzi Araghi S. Daliri M. Bahmanpour
  In this paper, we propose a method to approximate the solution of a linear Fredholm integro-differential equation by using the Chebyshev wavelet of the first kind as basis. For this purpose, we introduce the first Chebyshev operational matrix of integration. Chebyshev w چکیده کامل

  In this paper, we propose a method to approximate the solution of a linear Fredholm integro-differential equation by using the Chebyshev wavelet of the first kind as basis. For this purpose, we introduce the first Chebyshev operational matrix of integration. Chebyshev wavelet approximating method is then utilized to reduce the integro-differential equation to a system of algebraic equations. Illustrative examples are included to demonstrate the advantages and applicability of the technique. پرونده مقاله
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  30 - HYBRID OF RATIONALIZED HAAR FUNCTIONS METHOD FOR SOLVING DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER
  Y. Ordokhani N. Rahimi
  Abstract. In this paper, we implement numerical solution of differential equations of frac- tional order based on hybrid functions consisting of block-pulse function and rationalized Haar functions. For this purpose, the properties of hybrid of rationalized Haar function چکیده کامل

  Abstract. In this paper, we implement numerical solution of differential equations of frac- tional order based on hybrid functions consisting of block-pulse function and rationalized Haar functions. For this purpose, the properties of hybrid of rationalized Haar functions are presented. In addition, the operational matrix of the fractional integration is obtained and is utilized to convert computation of fractional differential equations into some algebraic equa- tions. We evaluate application of present method by solving some numerical examples. پرونده مقاله
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  31 - HAAR WAVELET AND ADOMAIN DECOMPOSITION METHOD FOR THIRD ORDER PARTIAL DIFFERENTIAL EQUATIONS ARISING IN IMPULSIVE MOTION OF A AT PLATE
  I. Singh S. Kumar
  We present here, a Haar wavelet method for a class of third order partial dierentialequations (PDEs) arising in impulsive motion of a flat plate. We also, present Adomaindecomposition method to find the analytic solution of such equations. Efficiency andaccuracy have be چکیده کامل

  We present here, a Haar wavelet method for a class of third order partial dierentialequations (PDEs) arising in impulsive motion of a flat plate. We also, present Adomaindecomposition method to find the analytic solution of such equations. Efficiency andaccuracy have been illustrated by solving numerical examples. پرونده مقاله
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  32 - NUMERICAL SOLUTION OF DELAY INTEGRAL EQUATIONS BY USING BLOCK PULSE FUNCTIONS ARISES IN BIOLOGICAL SCIENCES
  M. Nouri K. Maleknejad
  This 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 کامل

  This 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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  33 - A STRONG COMPUTATIONAL METHOD FOR SOLVING OF SYSTEM OF INFINITE BOUNDARY INTEGRO-DIFFERENTIAL EQUATIONS
  M. Matinfar Abbas Riahifar H. Abdollahi
  The introduced method in this study consists of reducing a system of infinite boundary integro-differential equations (IBI-DE) into a system of al- gebraic equations, by expanding the unknown functions, as a series in terms of Laguerre polynomials with unknown coeffi چکیده کامل

  The introduced method in this study consists of reducing a system of infinite boundary integro-differential equations (IBI-DE) into a system of al- gebraic equations, by expanding the unknown functions, as a series in terms of Laguerre polynomials with unknown coefficients. Properties of these polynomials and operational matrix of integration are rst presented. Finally, two examples illustrate the simplicity and the effectiveness of the proposed method have been presented. پرونده مقاله
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  34 - Direct method for solving nonlinear two-dimensional Volterra-Fredholm integro-differential equations by block-pulse functions
  Elnaz Poorfattah Akbar Jafari Shaerlar
  In this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional Volterra-Fredholm integro-differential equations. Here, we use the so-called two-dimensional block-pulse functions.First, the two-dimensional block-pulse operationa چکیده کامل

  In this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional Volterra-Fredholm integro-differential equations. Here, we use the so-called two-dimensional block-pulse functions.First, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. Then, by using this matrices, the nonlinear two-dimensional Volterra-Fredholm integro-differential equation has been reduced to an algebraic system. Some numerical examples are presented to illustrate the effectiveness and accuracy of the method پرونده مقاله