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Abstract and Applied Analysis
Volume 2014, Article ID 427023, 7 pages
Research Article

Symplectic Schemes for Linear Stochastic Schrödinger Equations with Variable Coefficients

1School of Mathematical Sciences, Dezhou University, Dezhou 253023, China
2The Center of Data Processing and Analyzing, Dezhou University, Dezhou 253023, China

Received 16 December 2013; Accepted 4 April 2014; Published 22 April 2014

Academic Editor: Adem Kılıçman

Copyright © 2014 Xiuling Yin and Yanqin Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper proposes a kind of symplectic schemes for linear Schrödinger equations with variable coefficients and a stochastic perturbation term by using compact schemes in space. The numerical stability property of the schemes is analyzed. The schemes preserve a discrete charge conservation law. They also follow a discrete energy transforming formula. The numerical experiments verify our analysis.