Numerical analysis of a conservative linear compact difference scheme for the coupled Schrödinger–Boussinesq equations

Abstract

ABSTRACTIn this article, a decoupled and linearized compact difference scheme is investigated to solve the coupled Schrödinger–Boussinesq equations numerically. We establish the convergence rates for the error at the order of in the -norm with the time step τ and mesh size h. The linear scheme is proved to conserve the total energy which is defined as a recursion relationship. Due to the difficulty in obtaining the priori estimate from the discrete energy, we utilize cut-off function technique to prove the convergence. The numerical results are reported to verify the theoretical analysis, and the numerical comparison between our scheme with previous methods are conducted to show the efficiency of our scheme.