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

Authors : Azim RİVAZ, Samane JAHAN ARA, Farzaneh YOUSEFİ

Pages : 0-0

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Publication Date : 2015-11-01

Article Type : Research Paper

Abstract :In this paper, we present a new approach to obtain the numerical solution of the linear twodimensional Fredholm and Volterra integro-differential equations insert ignore into journalissuearticles values(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