# New scheme for nonlinear Schrödinger equations with variable coefficients

Volume 19, Issue 3, pp 151--157 Publication Date: May 17, 2019       Article History
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### 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.

### Keywords

• Schrödinger equation
• finite element method
• finite difference scheme

•  65M06
•  65M12
•  65Z05

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