Strong convergence rate of splitting schemes for stochastic nonlinear Schrodinger equations

doi:10.1016/j.jde.2018.10.034

	Strong convergence rate of splitting schemes for stochastic nonlinear Schrodinger equations
	Cui, Jianbo 1,2; Hong, Jialin1,2 ; Liu, Zhihui 1,2,4; Zhou, Weien 3,5
	2019-04-15
发表期刊	JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN	0022-0396
卷号	266 期号:9 页码:5625-5663
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.
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
语种	英语
资助项目	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研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000458515200015
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/32369
专题	计算数学与科学工程计算研究所
通讯作者	Cui, Jianbo
作者单位	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
推荐引用方式 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.