Solution of an integro-differential nonlinear equation of Volterra arising of earthquake model

Abstract

In this paper, we study a new type of modeling of an Earthquake phenomenon, a mechanical model of the earthquake process in one-dimension using usual mathematical functions, the latter leads to the study of nonlinear integro-differential equation of Volterra. The existence and the uniqueness of the solution are proved. Using Nystrom method is builded to approximate the solution. The numerical tests show the effectiveness of this type of modeling.