High-order linear compact conservative method for the nonlinear Schrödinger equation coupled with the nonlinear Klein–Gordon equation

In this paper, we design a linear-compact conservative numerical scheme which preserves the original conservative properties to solve the Klein–Gordon–Schrödinger equation. The proposed scheme is based on using the finite difference method. The scheme is three-level and linear-implicit. Priori estimate and the convergence of the finite difference approximate solutions are discussed by the discrete energy method. Numerical results demonstrate that the present scheme is conservative, efficient and of high accuracy.