The Newton-Kantorovich method for Non-linear System of third order partial differential equations

In this paper we generalized Newton-Kantorovich method to be applied to a third order nonlinear system of partial differential equations (PDEs), then we discuss the stability analysis of this method. The generalized (N-K) is applied to the KdV (Korteweg-de Vries) equations and the general KdV system of nonlinear equations. The numerical solutions of these two systems are obtained by using the Matlab. The numerical results are compared with the exact solutions. We deduce that our results are fairly good approximations to the exact solution. These facts are reported in tables and figures.