Application of the Chebyshev polynomial in solving Fredholm integral equations

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.