Fourier spectral method with an adaptive time strategy for nonlinear fractional Schrödinger equation

Abstract

AbstractIn this paper, a Fourier spectral method with an adaptive time step strategy is proposed to solve the fractional nonlinear Schrödinger (FNLS) equation with periodic initial value problem. First, we prove the conservation law of the mass and the energy for the semi‐discrete Fourier spectral scheme. Second, the error estimation of the semi‐discrete scheme is given in the relevant fractional Sobolev space. Then, an adaptive time‐step strategy is designed to reduce central processing unit (CPU) time. Finally, the numerical experiments for the one‐, two‐ and three‐dimensional FNLSs, show that the adaptive strategy, compared to the constant time step, can reduce the CPU‐time by almost half.