Efficient energy‐preserving methods for the Schrödinger‐Boussinesq equation

Abstract

In this paper, we present two novel energy‐preserving schemes for the Schrödinger‐Boussinesq system based on the second‐order Adams prediction‐correction method. We first introduce supplementary variables to the initial model simultaneous its invariants to obtain a consistent and structural stable system. Then, we discretize the extended system by directly using the Fourier pseudo‐spectral method in space and second‐order Adams prediction‐correction method in time to construct conservative schemes. Numerical results show that the proposed schemes can reach second‐order accuracy and can conserve the discrete invariants very well.