Convergence of a high-order compact finite difference scheme for the Klein-Gordon-Schrodinger equations

In this paper, a conservative and linearly implicit finite difference scheme with second order temporal accuracy and eighth order spatial accuracy by means of the Richardson extrapolation method is proposed for approximating solution to the initial-boundary problem for the Klein-Gordon-Schrodinger equations. Furthermore, the difference solution is shown to be bounded by taking advantage of the fact that the proposed scheme possesses two conservation laws, and with the aid of the discrete energy method, the difference scheme is demonstrated to be convergent in the maximum norm. Finally, numerical experiments are assigned to support the theoretical results. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.