Numerical solution of Fredholm integral equations by using Bernstein polynomials

A numerical solution to solve Fredholm integral equation is presented in this work. The method is based on the replacement of unknown functions through Bernstein polynomials. The collocation method transforms the Fredholm equations into a system of algebraic equations. Also, convergence and rate of convergence are given. The procedure has great potential to be implemented in more complex systems where there are no exact solutions available except approximations.