Existence and uniqueness of the solution of an integro-differential equation of the second order with boundary conditions

Abstract In this paper we investigate the existence and approximation solution for nonlinear system of an integro-differential equation of the second order with boundary conditions by using the numerical-analytic method for investigating a system of nonlinear differential equation with boundary conditions which is given by Samoilenko A. M. And also these investigations lead us to generalized the above method.