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
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Accepted: 19 February 2019
Published online: 30 May 2019
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.
© Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2019