Numerical solution of non-linear Volterra integral equation of the first kind

Abstract

In this paper, we focus on the numerical solution of a nonlinear Volterra equation of the first kind. The existence and uniqueness of the exact solution is ensured under a necessary condition which we present next. We develop a numerical method based on two essential parts which are linearization and discretization. We start with the discretization of the equations using the concept of Nystrom's method and for the linearization we apply Newton's method. We present theorems that show the convergence of the proposed method. At the end, numerical  examples are presented to show the eficiency of our method.