Symplectic schemes for linear stochastic Schrödinger equations with variable coefficients. (English) Zbl 1470.65178

Summary: 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.


65M75 Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs
35Q41 Time-dependent Schrödinger equations and Dirac equations
65P10 Numerical methods for Hamiltonian systems including symplectic integrators
35R60 PDEs with randomness, stochastic partial differential equations
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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