A numerical scheme for Fredholm integral equations

Abstract

A different numerical method for nonlinear Fredholm integral equations of the second kind with the continuous kernel is considered. The main idea is to convert the integral equation problem into an optimization problem. Then by using an embedding method, the class of admissible trajectories is replaced by a class of positive Borel measures. The optimization problem in measure space is then approximated by a finite dimensional linear programming (LP) problem. Some examples demonstrate the effectiveness of the method.