Unconditional L~∞ convergence of a conservative compact finite difference scheme for the N-coupled Schroedinger-Boussinesq equations

摘要

In this paper, a conservative compact finite difference scheme is presented for solving the N-coupled nonlinear Schrodinger-Boussinesq equations. By using the discrete energy method, it is proved that our scheme is unconditionally convergent in the maximum norm and the convergent rate is at O(tau(2) + h(4)) with time step tau and mesh size h. Numerical results including the comparisons with other numerical methods are reported to demonstrate the accuracy and efficiency of the method and to confirm our theoretical analysis. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.