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Strong convergence rate of splitting schemes for stochastic nonlinear Schrodinger equations
Cui, Jianbo1,2; Hong, Jialin1,2; Liu, Zhihui1,2,4; Zhou, Weien3,5
2019-04-15
Source PublicationJOURNAL OF DIFFERENTIAL EQUATIONS
ISSN0022-0396
Volume266Issue:9Pages:5625-5663
AbstractIn 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.
KeywordStochastic nonlinear Schrodinger equation Strong convergence rate Exponential integrability Splitting scheme Non-monotone coefficients
DOI10.1016/j.jde.2018.10.034
Language英语
Funding ProjectNational Natural Science Foundation of China[91530118] ; National Natural Science Foundation of China[91130003] ; National Natural Science Foundation of China[11021101] ; National Natural Science Foundation of China[91630312] ; National Natural Science Foundation of China[11290142]
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000458515200015
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
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Cited Times:3[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/32369
Collection计算数学与科学工程计算研究所
Affiliation1.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
Recommended Citation
GB/T 7714
Cui, Jianbo,Hong, Jialin,Liu, Zhihui,et al. Strong convergence rate of splitting schemes for stochastic nonlinear Schrodinger equations[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2019,266(9):5625-5663.
APA Cui, Jianbo,Hong, Jialin,Liu, Zhihui,&Zhou, Weien.(2019).Strong convergence rate of splitting schemes for stochastic nonlinear Schrodinger equations.JOURNAL OF DIFFERENTIAL EQUATIONS,266(9),5625-5663.
MLA Cui, Jianbo,et al."Strong convergence rate of splitting schemes for stochastic nonlinear Schrodinger equations".JOURNAL OF DIFFERENTIAL EQUATIONS 266.9(2019):5625-5663.
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