Error analysis of a time fourth-order exponential wave integrator Fourier pseudo-spectral method for the nonlinear Dirac equation

Abstract

In this paper, we propose a time fourth-order exponential wave integrator (EWI) Fourier pseudo-spectral method for solving the nonlinear Dirac equation with periodic boundary value conditions. The new numerical method is designed by using Fourier pseudo-spectral method for spatial derivatives combined with a new fourth-order EWI for temporal derivatives. We give rigourously error analysis and establish error bounds for the numerical solutions without any CFL-type condition constraint. In more details, the proposed method has the fourth-order temporal accuracy and spectral spatial accuracy, respectively, in general -norm. Extensive numerical experiments are reported to confirm the theoretical analysis and show the superiority of the new method.