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NUMERICAL ANALYSIS ON ERGODIC LIMIT OF APPROXIMATIONS FOR STOCHASTIC NLS EQUATION VIA MULTI-SYMPLECTIC SCHEME
Hong, Jialin1; Wang, Xu1; Zhang, Liying2
2017
Source PublicationSIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN0036-1429
Volume55Issue:1Pages:305-327
AbstractWe consider a finite dimensional approximation of the stochastic nonlinear Schrodinger equation driven by multiplicative noise, which is derived by applying a symplectic method to the original equation in spatial direction. Both the unique ergodicity and the charge conservation law for this finite dimensional approximation are obtained on the unit sphere. To simulate the ergodic limit over long time for the finite dimensional approximation, we discretize it further in the temporal direction to obtain a fully discrete scheme, which inherits not only the stochastic multi-symplecticity and charge conservation law of the original equation but also the unique ergodicity of the finite dimensional approximation. The temporal average of the fully discrete numerical solution is proved to converge to the ergodic limit with order 1 with respect to the time step for a fixed spatial step. Numerical experiments verify our theoretical results on charge conservation, ergodicity, and weak convergence.
Keywordstochastic Schriidinger equation multiplicative noise unique ergodicity multisymplectic scheme weak error
DOI10.1137/16M1079099
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[11290142] ; National Natural Science Foundation of China[11601514]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000396683300014
PublisherSIAM PUBLICATIONS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/24833
Collection计算数学与科学工程计算研究所
Corresponding AuthorWang, Xu
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China
2.China Univ Min & Technol, Coll Sci, Dept Math, Beijing 100083, Peoples R China
Recommended Citation
GB/T 7714
Hong, Jialin,Wang, Xu,Zhang, Liying. NUMERICAL ANALYSIS ON ERGODIC LIMIT OF APPROXIMATIONS FOR STOCHASTIC NLS EQUATION VIA MULTI-SYMPLECTIC SCHEME[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2017,55(1):305-327.
APA Hong, Jialin,Wang, Xu,&Zhang, Liying.(2017).NUMERICAL ANALYSIS ON ERGODIC LIMIT OF APPROXIMATIONS FOR STOCHASTIC NLS EQUATION VIA MULTI-SYMPLECTIC SCHEME.SIAM JOURNAL ON NUMERICAL ANALYSIS,55(1),305-327.
MLA Hong, Jialin,et al."NUMERICAL ANALYSIS ON ERGODIC LIMIT OF APPROXIMATIONS FOR STOCHASTIC NLS EQUATION VIA MULTI-SYMPLECTIC SCHEME".SIAM JOURNAL ON NUMERICAL ANALYSIS 55.1(2017):305-327.
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