Exponential integrator preserving mass boundedness and energy conservation for nonlinear Schrödinger equation

Abstract

In this paper, a novel linearly implicit conservative scheme is developed for the two-dimensional nonlinear Schrödinger equation. The scheme is based on a new linearly implicit exponential time differencing method for the temporal discretization and the Fourier pseudo-spectral approximation for the spatial derivative. By rigorous analysis, we prove that the proposed scheme can preserve the energy conservation. Furthermore, although in fact the proposed scheme does not preserve mass conservation, we can prove that it can preserve the discrete L2 norm boundedness of the numerical solution, which may be helpful for the analysis of unconditional convergence of the energy conservative scheme. Then an optimal error estimate of the proposed scheme is established without any restriction on the grid ration. Numerical experiments show that the proposed scheme is remarkable efficiency comparing with some other existing structure-preserving schemes.