    August  2019, 24(8): 4295-4315. doi: 10.3934/dcdsb.2019120

## Convergence analysis of a symplectic semi-discretization for stochastic nls equation with quadratic potential

 1 LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China 2 School of Mathematical Science, University of Chinese Academy of Sciences, Beijing, 100049, China 3 School of Mathematics, Liaoning Normal University, Dalian, 116029, China 4 Department of Mathematics, College of Sciences, China University of Mining and Technology, Beijing, 100083, China

* Corresponding author: Lijun Miao

Dedicated to Peter Kloeden's 70th Birthday

Received  March 2018 Revised  February 2019 Published  June 2019

Fund Project: The first author is supported by the NNSFC (NO. 91530118, NO. 11290142 and NO. 91630312). The third author is supported by the NNSFC (NO.11601514, NO.11801556 and NO.11771444).

In this paper, we investigate the convergence in probability of a stochastic symplectic scheme for stochastic nonlinear Schrödinger equation with quadratic potential and an additive noise. Theoretical analysis shows that our symplectic semi-discretization is of order one in probability under appropriate regularity conditions for the initial value and noise. Numerical experiments are given to simulate the long time behavior of the discrete averaged charge and energy as well as the influence of the external potential and noise, and to test the convergence order.

Citation: Jialin Hong, Lijun Miao, Liying Zhang. Convergence analysis of a symplectic semi-discretization for stochastic nls equation with quadratic potential. Discrete & Continuous Dynamical Systems - B, 2019, 24 (8) : 4295-4315. doi: 10.3934/dcdsb.2019120
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##### References:
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