Mean-square convergence of a symplectic local discontinuous Galerkin method applied to stochastic linear Schrodinger equation

doi:10.1093/imanum/drw023

	Mean-square convergence of a symplectic local discontinuous Galerkin method applied to stochastic linear Schrodinger equation
	Chen, Chuchu1 ; Hong, Jialin1 ; Ji, Lihai 2
	2017-04-01
发表期刊	IMA JOURNAL OF NUMERICAL ANALYSIS
ISSN	0272-4979
卷号	37 期号:2 页码:1041-1065
摘要	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.
关键词	symplectic method local discontinuous Galerkin method stochastic linear Schrodinger equation L-2-stability charge conservation law mean-square convergence
DOI	10.1093/imanum/drw023
语种	英语
资助项目	NNSFC[91130003] ; NNSFC[11021101] ; NNSFC[11290142] ; NNSFC[11471310]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000401009800015
出版者	OXFORD UNIV PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/26011
专题	计算数学与科学工程计算研究所
通讯作者	Ji, Lihai
作者单位	1.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
推荐引用方式 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.