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

Year 2015, Volume: 12 Issue: 2, - , 01.11.2015

Azim Rivaz , Samane Jahan Ara Farzaneh Yousefi

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

Keywords

Two-dimensional Fredholm and Volterra integro-differential equations, Two-dimensional Chebyshev polynomials, Operational matrix of integration

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