Approximate Solution of a Class of Nonlinear Volterra Integral Equations

In this paper we introduce an approach by an optimization method to find approximate solution for a class of nonlinear Volterra integral equations of the first and second kind. To this purpose, we consider two stages of approximation. First we convert the integral equation to a moment problem and then we modify the new problem to two classes of optimization problems, non-constraint optimization problems and optimal control problems. Finally numerical examples is proposed.