KMS Of Academy of mathematics and systems sciences, CAS
| Strong convergence rate of splitting schemes for stochastic nonlinear Schrodinger equations | |
Cui, Jianbo1,2; Hong, Jialin1,2 ; Liu, Zhihui1,2,4; Zhou, Weien3,5
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| 2019-04-15 | |
| Source Publication | JOURNAL OF DIFFERENTIAL EQUATIONS
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| ISSN | 0022-0396 |
| Volume | 266Issue:9Pages:5625-5663 |
| Abstract | 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. |
| Keyword | Stochastic nonlinear Schrodinger equation Strong convergence rate Exponential integrability Splitting scheme Non-monotone coefficients |
| DOI | 10.1016/j.jde.2018.10.034 |
| Language | 英语 |
| Funding Project | National 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 Area | Mathematics |
| WOS Subject | Mathematics |
| WOS ID | WOS:000458515200015 |
| Publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/32369 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Cui, Jianbo |
| Affiliation | 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 |
| 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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