On the weakly singular integro-differential nonlinear Volterra equation depending in acceleration term

Abstract

In this article, our study deals with the existence and the uniqueness of the solution of a second degree integro-differential nonlinear Volterra equation with a weakly singular kernel, i.e., the solution depends on its speed (first derivative) and its acceleration (second derivative); whereas using Nystrom method and product integration method with piecewise projection, we approximate this solution.