Application of the Chebyshev polynomial in solving Fredholm integral equations

Abstract

In this paper the Fredholm integral equation of the second kind is solved, where Chebyshev polynomials are applied to approximate a solution for an unknown function in the Fredholm integral equation and convert this equation to a system of linear equations. Also, convergence and rate of convergence are given. The accuracy of this method is verified through some numerical examples and the results are compared to a previous result set to investigate the effects of choosing Chebyshev and Legendre polynomials.