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.
Xiuling Yin. Yanqin Liu. "Symplectic Schemes for Linear Stochastic Schrödinger Equations with Variable Coefficients." Abstr. Appl. Anal. 2014 (SI08) 1 - 7, 2014. https://doi.org/10.1155/2014/427023