Eur. Phys. J. Plus (2019) 134: 244
https://doi.org/10.1140/epjp/i2019-12584-3

Regular Article

A high-order split-step finite difference method for the system of the space fractional CNLS

School of Mathematics and Statistics, Zhengzhou University, 450001, Zhengzhou, China

^* e-mail: limeng@zzu.edu.cn

Received: 25 July 2018
Accepted: 19 February 2019
Published online: 30 May 2019

Abstract

In this paper, the schemes based on the high-order quasi-compact split-step finite difference methods are derived for the one- and two-dimensional coupled fractional Schrödinger equations. In order to improve the computing efficiency, we adopt the split-step method for handling the nonlinearity. By using a high-order quasi-compact scheme in space, the numerical method improves the accuracy effectively. We prove the conservation laws, prior boundedness and unconditional error estimates of the quasi-compact finite difference scheme for the linear problem. Moreover, for the nonlinear problem, we show that the quasi-compact split-step finite difference method can also keep the conservation law in the mass sense. For solving the multi-dimensional problem, we combine the quasi-compact split-step method with the alternating direction implicit technique. At last, numerical examples are performed to illustrate our theoretical results and show the efficiency of the proposed schemes.