Application of Chebyshev polynomials for solving nonlinear Volterra-Fredholm integral equations system and convergence analysis

R  Ezzati   and S  Najafalizadeh

doi:10.17485/ijst/2012/v5i2.8

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Application of Chebyshev polynomials for solving nonlinear Volterra-Fredholm integral equations system and convergence analysis

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Indian Journal of Science and Technology

DOI: 10.17485/ijst/2012/v5i2.8

Year: 2012, Volume: 5, Issue: 2, Pages: 1-5

Original Article

Application of Chebyshev polynomials for solving nonlinear Volterra-Fredholm integral equations system and convergence analysis

R. Ezzati^1* and S. Najafalizadeh²

^1,2Department of Mathematics, [email protected]*
*Author For Correspondence
R. Ezzati
^1,2Department of Mathematics,
Email:[email protected]*

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

n this paper, we solve the nonlinear Volterra-Fredholm integral equations system by using the Chebyshev polynomials. First we introduce the Chebyshev polynomials and approximate functions via their application. Then, we use Chebyshev polynomials as a collocation basis to change the nonlinear Volterra-Fredholm integral equations system to a system of nonlinear algebraic equations. Finally, the convergence analysis is considered, and numerical examples given to illustrate the efficiency of this method.
Keywords: Volterra-Fredholm; System of integral equations; Chebyshev polynomials; Operational matrix