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Volume 11, Issue 2
Numerical Solution of Two-dimensional Nonlinear Volterra Integro-differential Equations by Tau Method

Y. Ordokhani and F. Samari

J. Info. Comput. Sci. , 11 (2016), pp. 101-110.

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  • Abstract
In this paper, a method is employed to approximate the solution of two-dimensional nonlinear Volterra integro-differential equations (2DNVIDEs) with supplementary conditions. First, we introduce two- dimensional Legendre polynomials, then convert 2DNVIDEs to the two-dimensional linear Volterra integro- differential equations (2DLVIDEs). Using this properties and collocation points, reduce it to the system of algebraic equations. Finally, some numerical examples are given to clarify the efficiency and accuracy of the present method.
  • Keywords

Two dimensional, Linear, Nonlinear, Volterra integro-differential equation, Tau method .

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COPYRIGHT: © Global Science Press

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@Article{JICS-11-101, author = {Y. Ordokhani and F. Samari}, title = {Numerical Solution of Two-dimensional Nonlinear Volterra Integro-differential Equations by Tau Method}, journal = {Journal of Information and Computing Science}, year = {2024}, volume = {11}, number = {2}, pages = {101--110}, abstract = {In this paper, a method is employed to approximate the solution of two-dimensional nonlinear Volterra integro-differential equations (2DNVIDEs) with supplementary conditions. First, we introduce two- dimensional Legendre polynomials, then convert 2DNVIDEs to the two-dimensional linear Volterra integro- differential equations (2DLVIDEs). Using this properties and collocation points, reduce it to the system of algebraic equations. Finally, some numerical examples are given to clarify the efficiency and accuracy of the present method. }, issn = {1746-7659}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jics/22518.html} }
TY - JOUR T1 - Numerical Solution of Two-dimensional Nonlinear Volterra Integro-differential Equations by Tau Method AU - Y. Ordokhani and F. Samari JO - Journal of Information and Computing Science VL - 2 SP - 101 EP - 110 PY - 2024 DA - 2024/01 SN - 11 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jics/22518.html KW - Two dimensional, Linear, Nonlinear, Volterra integro-differential equation, Tau method . AB - In this paper, a method is employed to approximate the solution of two-dimensional nonlinear Volterra integro-differential equations (2DNVIDEs) with supplementary conditions. First, we introduce two- dimensional Legendre polynomials, then convert 2DNVIDEs to the two-dimensional linear Volterra integro- differential equations (2DLVIDEs). Using this properties and collocation points, reduce it to the system of algebraic equations. Finally, some numerical examples are given to clarify the efficiency and accuracy of the present method.
Y. Ordokhani and F. Samari. (2024). Numerical Solution of Two-dimensional Nonlinear Volterra Integro-differential Equations by Tau Method. Journal of Information and Computing Science. 11 (2). 101-110. doi:
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