A New Technique for Approximate Solutions of the Nonlinear Volterra Integral Equations of the Second Kind

In this paper, a different approach for finding an approximate solution of the Nonlinear Volterra Integral Equations (NVIE) of the Second Kind is presented. In this approach, the nonlinearity of the kernel has no serious effect on the convergence of the solution. The author's approach is simple and direct for solving the (NVIE). The solution of the original problem is obtained, by converting the problem into an optimal moment problem. The moment problem is modified into one consisting of the minimization of a positive linear functional over a set of Radon measures. Then, an optimal measure is obtained, which is approximated by a finite combination of atomic measures and, by using atomic measures, this one is changed into a semi-infinite dimensional nonlinear programming problem. The latter is approximated by a finite dimensional linear programming problem. Finally, the approximated solution for some examples is found.