Iteration methods for Fredholm integral equations of the second kind

In this paper, we propose an efficient iteration algorithm for Fredholm integral equations of the second kind. We show that for every step of iteration the coefficient matrix of the linear system to be inverted remains the same as in the original approximation methods, while we obtain the superconvergence rates for every step of iteration. We apply our iteration methods to various approximation methods such as degenerate kernel methods, Galerkin, collocation and new projection methods. We illustrate our results by numerical experiments.