An exponential wave integrator Fourier pseudospectral method for the nonlinear Schr?dinger equation with wave operator

摘要

In this article, an exponential wave integrator Fourier pseudospectral (EWI-FP) method is proposed for solving the nonlinear Schr?dinger equation with wave operator. The numerical method is based on a Deuflhard-type exponential wave integrator for temporal integration and the Fourier pseudospectral method for spatial discretizations. The scheme is fully explicit and very efficient thanks to the fast Fourier transform. Numerical analysis of the proposed EWI-FP method is carried out and rigorous error estimates are established by means of the mathematical induction. Numerical results are reported to confirm the theoretical studies.