Efficient and conservative compact difference scheme for the coupled Schrodinger-Boussinesq equations

In this paper, we construct an efficient and conservative compact difference scheme based on the scalar auxiliary variable (SAV) approach for the coupled Schrodinger-Boussinesq (CSB) equations. The presented scheme preserves the discrete modified energy. We prove the convergent rates of second-order in time and fourth-order in space by using the discrete energy method in detail. Some numerical experiments are given to verify our theoretical analysis. (C) 2022 IMACS. Published by Elsevier B.V. All rights reserved.

Automated summary

In this paper, an efficient and conservative compact difference scheme based on the scalar auxiliary variable (SAV) approach is proposed for solving the coupled Schrodinger-Boussinesq (CSB) equations. The scheme preserves the discrete modified energy and the convergent rates of second-order in time and fourth-order in space are proven using the discrete energy method. Numerical experiments are conducted to validate the theoretical analysis.