Error Analysis and Numerical Simulations of Strang Splitting Method for Space Fractional Nonlinear Schrödinger Equation

Abstract

In this paper, we study a fast explicit operator splitting method for space fractional nonlinear Schrodinger equation in one (1D), two (2D) and three dimensions (3D) with periodic boundary conditions. The equation is split into linear and nonlinear parts: the linear part is solved by the Fourier spectral method, which is based on the exact solution and thus has no stability restriction on the time-step size; the nonlinear subequation is then solved analytically due to the availability of a closed-form solution. The rigorous analysis of the discrete mass conservation principle and the convergence rate of the proposed algorithm are proved. The theoretical results show the proposed method is $$L^2$$ unconditionally stable, second order accurate in time, whereas the spatial accuracy depends on the regularity of the solution. Numerical experiments for 1D, 2D and 3D cases demonstrate the efficiency of the proposed method.