Two-dimensional Chebyshev Polynomials for Solving Two-dimensional Integro-Differential Equations

Abstract

In this paper, we present a new approach to obtain the numerical solution of the linear twodimensional Fredholm and Volterra integro-differential equations (2D-FIDE and 2D-VIDE). First, we introduce the two-dimensional Chebyshev polynomials and construct their operational matrices of integration. Then, both of them, two-dimensional Chebyshev polynomials and their operational matrix of integration, are used to represent the matrix form of 2D-FIDE and 2D-VIDE. The main characteristic of this approach is that it reduces 2D-FIDE and 2D-VIDE to a system of linear algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the presented technique