On error estimates of an exponential wave integrator sine pseudospectral method for the Klein–Gordon–Zakharov system

Abstract

In this article, we propose an exponential wave integrator sine pseudospectral (EWI‐SP) method for solving the Klein–Gordon–Zakharov (KGZ) system. The numerical method is based on a Deuflhard‐type exponential wave integrator for temporal integrations and the sine pseudospectral method for spatial discretizations. The scheme is fully explicit, time reversible and very efficient due to the fast algorithm. Rigorous finite time error estimates are established for the EWI‐SP method in energy space with no CFL‐type conditions which show that the method has second order accuracy in time and spectral accuracy in space. Extensive numerical experiments and comparisons are done to confirm the theoretical studies. Numerical results suggest the EWI‐SP allows large time steps and mesh size in practical computing. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 266–291, 2016