Discussion on convergence of Legendre polynomial for numerical solution of integral equations

In this article, a numerical solution of Fredholm integral equation of the second kind will be discussed, for this result, we choose Legendre polynomials as basis functions and collocation method to estimate a solution for an unknown function in this equation. Convergence of this method and rate of convergence will be investigated. Finally, some numerical examples will be stated to show the accuracy of this method.