# Structure-preserving splitting methods for stochastic logarithmic Schrödinger equation via regularized energy approximation

@article{Cui2021StructurepreservingSM, title={Structure-preserving splitting methods for stochastic logarithmic Schr{\"o}dinger equation via regularized energy approximation}, author={Jianbo Cui and Jialin Hong and Liying Sun}, journal={ArXiv}, year={2021}, volume={abs/2111.04402} }

In this paper, we study two kinds of structure-preserving splitting methods, including the Lie–Trotter type splitting method and the finite difference type method, for the stochastic logarithmic Schrödinger equation (SlogS equation) via a regularized energy approximation. We first introduce a regularized SlogS equation with a small parameter 0 < ǫ ≪ 1 which approximates the SlogS equation and avoids the singularity near zero density. Then we present a priori estimates, the regularized entropy…

## 2 Citations

### Analysis of a splitting scheme for a class of nonlinear stochastic Schrödinger equations

- MathematicsArXiv
- 2020

Some exponential moment bounds for the exact and numerical solutions are proved and this enables the analysis of a splitting scheme for a class of nonlinear stochastic Schrodinger equations driven by additive Ito noise to provide strong orders of convergence as well as Orders of convergence in probability and almost surely.

### Explicit Numerical Methods for High Dimensional Stochastic Nonlinear Schrödinger Equation: Divergence, Regularity and Convergence

- Computer Science, MathematicsArXiv
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This paper proves that the classical explicit numerical methods of high dimensional stochastic nonlinear Schrödinger equations are unstable and suffer from the numerical divergence phenomenon, and proposes a kind of explicit splitting numerical methods that is able to enhance the numerical stability.

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