Energy preserving relaxation method for space-fractional nonlinear Schrödinger equation

Abstract

In this paper, we develop and analyze an energy preserving relaxation scheme for a class of space fractional nonlinear Schrödinger equations (F-NLS) with periodic boundary condition. This scheme can preserve the discrete mass and energy for F-NLS with general power nonlinearity. The second order convergence in time direction for the numerical method is rigorously proved for the cubic nonlinear F-NLS. Some numerical simulations for 1D and 2D cases based on the Fourier spectral approximation in space are presented to validate the theoretical analysis of the proposed method.