Numerical development for an integro-diffirential equation depending in acceleration

Abstract

The objective of this dissertation is the analytical and numerical study of integro-differential equations by methods based on successive Picard methods. Our work is the generalization of other work of degrees 1 in the framework of nonlinear Volterra this kind of equations came from dynamic system especially the dynamic systems summarize the seismic problems, the cases studied in the previous work depend only on the speed and my work depends on velocity and acceleration, we get existence and uniqueness using Nyström adapt method to solve our problem.