Numerical Solution of Two-dimensional Nonlinear Volterra Integro-differential Equations by Tau Method

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.