Error estimates of exponential wave integrator sine pseudospectral method for Schrödinger–Boussinesq system

Abstract

In this article, an exponential wave integrator sine pseudospectral method is formulated and analysed for discretizing the coupled Schrödinger–Boussinesq system. Our method is based on the utilizations of sine pseudospectral discretization for spatial derivatives followed by exponential wave integrator for temporal derivatives in phase space. The scheme is fully explicit and very efficient due to discrete sine transform (DST), and it is of spectral accuracy in space and second-order accuracy in time. Numerical analysis of the proposed method is carried out and rigorous error estimates are established via discrete energy and induction argument method. The numerical results are reported to verify our theoretical analysis.