CONVERGENCE ANALYSIS OF A SYMPLECTIC SEMI-DISCRETIZATION FOR STOCHASTIC NLS EQUATION WITH QUADRATIC POTENTIAL

被引：1
作者：
Hong, Jialin [1 ,2 ]
Miao, Lijun [3 ]
Zhang, Liying [4 ]
机构：
[1] Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
[2] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
[3] Liaoning Normal Univ, Sch Math, Dalian 116029, Peoples R China
[4] China Univ Min & Technol, Coll Sci, Dept Math, Beijing 100083, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2019年 / 24卷 / 08期
关键词：
Stochastic nonlinear Schrodinger equation; quadratic potential; additive noise; stochastic symplectic scheme; convergence analysis; NONLINEAR SCHRODINGER-EQUATION; SEMIDISCRETE SCHEME; WEAK;
D O I：
10.3934/dcdsb.2019120
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we investigate the convergence in probability of a stochastic symplectic scheme for stochastic nonlinear Schrodinger 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.
引用
收藏
页码：4295 / 4315
页数：21
相关论文
共 17 条
  • [1] Anton C, 2014, ELECTRON T NUMER ANA, V43, P1
  • [2] EXPONENTIAL INTEGRATORS FOR STOCHASTIC SCHRODINGER EQUATIONS DRIVEN BY ITO NOISE
    Anton, Rikard
    Cohen, David
    [J]. JOURNAL OF COMPUTATIONAL MATHEMATICS, 2018, 36 (02) : 276 - 309
  • [3] MATHEMATICAL THEORY AND NUMERICAL METHODS FOR BOSE-EINSTEIN CONDENSATION
    Bao, Weizhu
    Cai, Yongyong
    [J]. KINETIC AND RELATED MODELS, 2013, 6 (01) : 1 - 135
  • [4] Belaouar R., 2015, STOCH PARTIAL DIFFER, V3, P103, DOI [10.1007/s40072-015-0044-z, DOI 10.1007/S40072-015-0044-Z]
  • [5] Critical nonlinear Schrodinger equations with and without harmonic potential
    Carles, R
    [J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2002, 12 (10) : 1513 - 1523
  • [6] Mean-square convergence of a symplectic local discontinuous Galerkin method applied to stochastic linear Schrodinger equation
    Chen, Chuchu
    Hong, Jialin
    Ji, Lihai
    [J]. IMA JOURNAL OF NUMERICAL ANALYSIS, 2017, 37 (02) : 1041 - 1065
  • [7] SYMPLECTIC RUNGE-KUTTA SEMIDISCRETIZATION FOR STOCHASTIC SCHRODINGER EQUATION
    Chen, Chuchu
    Hong, Jialin
    [J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2016, 54 (04) : 2569 - 2593
  • [8] Strong convergence rate of finite difference approximations for stochastic cubic Schrodinger equations
    Cui, Jianbo
    Hong, Jialin
    Liu, Zhihui
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 263 (07) : 3687 - 3713
  • [9] A semi-discrete scheme for the stochastic nonlinear Schrodinger equation
    De Bouard, A
    Debussche, A
    [J]. NUMERISCHE MATHEMATIK, 2004, 96 (04) : 733 - 770
  • [10] The stochastic nonlinear Schrodinger equation in H 1
    de Bouard, A
    Debussche, A
    [J]. STOCHASTIC ANALYSIS AND APPLICATIONS, 2003, 21 (01) : 97 - 126
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