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.
Acknowledgments
The authors are grateful to the anonymous reviewers for their valuable suggestions, which help improve this paper significantly.
Disclosure statement
No potential conflict of interest was reported by the author(s).