Exact and numerical solutions for coupled nonlinear Klein-Gordon-Schrödinger equations

Abstract

In this paper we give a derivation of the exact solution for coupled nonlinear Klein-Gordon-Schrödinger equation by the ansatz method. We present a numerical solution by implicit finite difference scheme which is fourth order accurate in space and second order in time. We discuss the accuracy and stability of the scheme. Numerical results are given to show that this method is quite accurate.