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Mean-square convergence of a symplectic local discontinuous Galerkin method applied to stochastic linear Schrodinger equation
Chen, Chuchu1; Hong, Jialin1; Ji, Lihai2
2017-04-01
Source PublicationIMA JOURNAL OF NUMERICAL ANALYSIS
ISSN0272-4979
Volume37Issue:2Pages:1041-1065
AbstractIn this article, we investigate the mean-square convergence of a novel symplectic local discontinuous Galerkin method in L-2-norm for stochastic linear Schrodinger equation with multiplicative noise. It is shown that the mean-square error is bounded, not only by the temporal and spatial step sizes, but also by their ratio. The mean-square convergence rate with respect to the computational cost is derived under appropriate assumptions for initial data and noise. Meanwhile, we show that the method preserves the discrete charge conservation law, which implies an L-2-stability.
Keywordsymplectic method local discontinuous Galerkin method stochastic linear Schrodinger equation L-2-stability charge conservation law mean-square convergence
DOI10.1093/imanum/drw023
Language英语
Funding ProjectNNSFC[91130003] ; NNSFC[11021101] ; NNSFC[11290142] ; NNSFC[11471310]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000401009800015
PublisherOXFORD UNIV PRESS
Citation statistics
Cited Times:2[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/26011
Collection计算数学与科学工程计算研究所
Affiliation1.Chinese Acad Sci, State Key Lab Sci & Engn Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100190, Peoples R China
2.Inst Appl Phys & Computat Math, Beijing 100094, Peoples R China
Recommended Citation
GB/T 7714
Chen, Chuchu,Hong, Jialin,Ji, Lihai. Mean-square convergence of a symplectic local discontinuous Galerkin method applied to stochastic linear Schrodinger equation[J]. IMA JOURNAL OF NUMERICAL ANALYSIS,2017,37(2):1041-1065.
APA Chen, Chuchu,Hong, Jialin,&Ji, Lihai.(2017).Mean-square convergence of a symplectic local discontinuous Galerkin method applied to stochastic linear Schrodinger equation.IMA JOURNAL OF NUMERICAL ANALYSIS,37(2),1041-1065.
MLA Chen, Chuchu,et al."Mean-square convergence of a symplectic local discontinuous Galerkin method applied to stochastic linear Schrodinger equation".IMA JOURNAL OF NUMERICAL ANALYSIS 37.2(2017):1041-1065.
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