Numerical analysis of a conservative linear compact difference scheme for the coupled Schrodinger-Boussinesq equations

In this article, a decoupled and linearized compact difference scheme is investigated to solve the coupled Schrodinger- Boussinesq equations numerically. We establish the convergence rates for the error at the order of O(t 2 + h4) in the l2- norm with the time step t 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.