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Tari, Abolfazl,Shahmorad, Sedaghat The Korean Society for Computational and Applied M 2012 Journal of applied mathematics & informatics Vol.30 No.3
In this work, we investigate solving two-dimensional nonlinear Volterra integral equations of the first kind (2DNVIEF). Here we convert 2DNVIEF to the two-dimensional linear Volterra integral equations of the first kind (2DLVIEF) and then we solve it by using operational approach of the Tau method. But for solving the 2DLVIEF we convert it to an equivalent equation of the second kind and then by giving some theorems we formulate the operational Tau method with standard base for solving the equation of the second kind. Finally, some numerical examples are given to clarify the efficiency and accuracy of presented method.
A MATRIX FORMULATION OF THE MIXED TYPE LINEAR VOLTERRA-FREDHOLM INTEGRAL EQUATIONS
Fazeli, S.,Shahmorad, S. The Korean Society for Computational and Applied M 2011 Journal of applied mathematics & informatics Vol.29 No.5
In this paper we present an operational method for solving linear Volterra-Fredholm integral equations (VFIE). The method is con- structed based on three matrices with simple structures which lead to a simple and high accurate algorithm. We also present an error estimation and demonstrate accuracy of the method by numerical examples.
M. Hosseini AliAbadi,S. Shahmorad 한국전산응용수학회 2002 Journal of applied mathematics & informatics Vol.9 No.2
In this paper we obtain the matrix Tau Method representation of a general boundary value problem for Fredholm and Volterra integro-differential equations of order $\nu$. Some theoretical results are given that simplify the application of the Tau Method. The application of the Tau Method to the numerical solution of such problems is shown. Numerical results and details of the algorithm confirm the high accuracy and user-friendly structure of this numerical approach. In this paper we obtain the matrix Tau Method representation of a general boundary value problem for Fredholm and Volterra integro-differential equations of order $\nu$. Some theoretical results are given that simplify the application of the Tau Method. The application of the Tau Method to the numerical solution of such problems is shown. Numerical results and details of the algorithm confirm the high accuracy and user-friendly structure of this numerical approach.
Aliabadi, M.-Hosseini,Shahmorad, S. 한국전산응용수학회 2002 The Korean journal of computational & applied math Vol.9 No.2
In this paper we obtain the matrix Tau Method representation of a general boundary value problem for Fredholm and Volterra integro-differential equations of order $\nu$. Some theoretical results are given that simplify the application of the Tau Method. The application of the Tau Method to the numerical solution of such problems is shown. Numerical results and details of the algorithm confirm the high accuracy and user-friendly structure of this numerical approach.
Solving system of generalized non-linear Volterra integro-differential equations
A. Khani,S. Shahmorad 장전수학회 2012 Advanced Studies in Contemporary Mathematics Vol.22 No.1
In this paper, we study a simple new method to nd numerical solution of the System of Non-linear Volterra Functional Integro-Dierential Equations (SNVFIDE) which is a generalization of [1]. To this end, we will present our method based on matrix form of SNVFIDE. Finally accuracy of the method is veried by presenting some numerical examples.
Abolfazl Tari,Sedaghat Shahmorad 한국전산응용수학회 2012 Journal of applied mathematics & informatics Vol.30 No.3
In this work, we investigate solving two-dimensional nonlinear Volterra integral equations of the first kind (2DNVIEF). Here we convert 2DNVIEF to the two-dimensional linear Volterra integral equations of the first kind (2DLVIEF) and then we solve it by using operational approach of the Tau method. But for solving the 2DLVIEF we convert it to an equivalent equation of the second kind and then by giving some theorems we formulate the operational Tau method with standard base for solving the equation of the second kind. Finally, some numerical examples are given to clarify the efficiency and accuracy of presented method.
A MATRIX FORMULATION OF THE MIXED TYPE LINEAR VOLTERRA-FREDHOLM INTEGRAL EQUATIONS
S. Fazeli,S. Shahmorad 한국전산응용수학회 2011 Journal of applied mathematics & informatics Vol.29 No.5
In this paper we present an operational method for solving linear Volterra-Fredholm integral equations (VFIE). The method is constructed based on three matrices with simple structures which lead to a simple and high accurate algorithm. We also present an error estimation and demonstrate accuracy of the method by numerical examples.