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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 Publication IMA JOURNAL OF NUMERICAL ANALYSIS ISSN 0272-4979 Volume 37Issue:2Pages:1041-1065 Abstract In 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. Keyword symplectic method local discontinuous Galerkin method stochastic linear Schrodinger equation L-2-stability charge conservation law mean-square convergence DOI 10.1093/imanum/drw023 Language 英语 Funding Project NNSFC[91130003] ; NNSFC[11021101] ; NNSFC[11290142] ; NNSFC[11471310] WOS Research Area Mathematics WOS Subject Mathematics, Applied WOS ID WOS:000401009800015 Publisher OXFORD UNIV PRESS Citation statistics Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/26011 Collection 计算数学与科学工程计算研究所 Corresponding Author Ji, Lihai Affiliation 1.Chinese Acad Sci, State Key Lab Sci & Engn Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100190, Peoples R China2.Inst Appl Phys & Computat Math, Beijing 100094, Peoples R China Recommended CitationGB/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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