New scheme for nonlinear Schrödinger equations with variable coefficients

Volume 19, Issue 3, pp 151--157 http://dx.doi.org/10.22436/jmcs.019.03.02
Publication Date: May 17, 2019 Submission Date: August 04, 2017 Revision Date: April 13, 2019 Accteptance Date: April 19, 2019

Authors

Xiu-Ling Yin - School of Mathematical Sciences, Dezhou University, Dezhou, China. Shu-Xia Kong - School of Mathematical Sciences, Dezhou University, Dezhou, China. Yan-Qin Liu - School of Mathematical Sciences, Dezhou University, Dezhou, China. Xiao-Tong Zheng - School of Statistics, Renmin University of China, Beijing, China.


Abstract

This paper proposes a numerical scheme for nonlinear Schrödinger equations with periodic variable coefficients and stochastic perturbation. The scheme is obtained by applying finite element method in spatial direction and finite difference scheme in temporal direction, respectively. The scheme is stable in the sense that it preserves discrete charge of the Schrödinger equations. The numerical examples verify the conservative property of the new scheme.


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