Strong convergence rate of splitting schemes for stochastic nonlinear Schrodinger equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:266

Article

Cui, Jianbo^1,2  Hong, Jialin^1,2  Liu, Zhihui^1,2,4  Zhou, Weien^3,5 

[1] Chinese Acad Sci, LSEC, Acad Math & Syst Sci, ICMSEC, Beijing 100190, Peoples R China

[2] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

[3] Natl Univ Def Technol, Coll Sci, Changsha, Hunan, Peoples R China

[4] Hong Kong Univ Sci & Technol, Dept Math, Kowloon, Clear Water Bay, Hong Kong, Peoples R China

[5] Natl Innovat Inst Def Technol, Unmanned Syst Res Ctr, Beijing, Peoples R China

关键词: Stochastic nonlinear Schrodinger equation;    Strong convergence rate;    Exponential integrability;    Splitting scheme;    Non-monotone coefficients;   

DOI  :  10.1016/j.jde.2018.10.034

来源: Elsevier

【 摘 要 】

In this paper, we show that solutions of stochastic nonlinear Schrodinger (NLS) equations can be approximated by solutions of coupled splitting systems. Based on these systems, we propose a new kind of fully discrete splitting schemes which possess algebraic strong convergence rates for stochastic NLS equations. Key ingredients of our approach are using the exponential integrability and stability of the corresponding splitting systems and numerical approximations. In particular, under very mild conditions, we derive the optimal strong convergence rate O(N-2 + tau(1/2)) of the spectral splitting Crank-Nicolson scheme, where N and tau denote the dimension of the approximate space and the time step size, respectively. (C) 2018 Elsevier Inc. All rights reserved.

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