A conservative compact difference scheme for the coupled Klein-Gordon-Schrödinger equation

In this article, a conservative compact difference scheme is presented for the periodic initial-value problem of Klein-Gordon-Schrodinger equation. On the basis of some inequalities about norms and the priori estimates, convergence of the difference solution is proved with order O(h(4) + tau(2)) in maximum norm. Numerical experiments demonstrate the accuracy and efficiency of the compact scheme. (C) 2013 Wiley Periodicals, Inc.