Symplectic Schemes for Linear Stochastic Schrödinger Equations with Variable Coefficients

Abstract

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.The paper is organized as follows. In Section 2, we give a symplectic structure of the LSES. In Section 3, we present the