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SYMPLECTIC RUNGE-KUTTA SEMIDISCRETIZATION FOR STOCHASTIC SCHRODINGER EQUATION
Chen, Chuchu; Hong, Jialin
2016
Source PublicationSIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN0036-1429
Volume54Issue:4Pages:2569-2593
AbstractBased on a variational principle with a stochastic forcing, we indicate that the stochastic Schrodinger equation in the Stratonovich sense is an infinite-dimensional stochastic Hamiltonian system, whose phase flow preserves symplecticity. We propose a general class of stochastic symplectic Runge-Kutta methods in the temporal direction to the stochastic Schrodinger equation in the Stratonovich sense and show that the methods preserve the charge conservation law. We present a convergence theorem on the relationship between the mean-square convergence order of a semi-discrete method and its local accuracy order. Taking the stochastic midpoint scheme as an example of stochastic symplectic Runge-Kutta methods in the temporal direction, based on the theorem we show that the mean-square convergence order of the semidiscrete scheme is 1 under appropriate assumptions.
Keywordstochastic Schrodinger equation infinite-dimensional stochastic Hamiltonian system symplectic structure symplectic Runge-Kutta method semidiscretization mean-square convergence order
DOI10.1137/151005208
Language英语
Funding ProjectNational Natural Science Foundation of China[91130003] ; National Natural Science Foundation of China[11021101] ; National Natural Science Foundation of China[11290142]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000385274300024
PublisherSIAM PUBLICATIONS
Citation statistics
Cited Times:8[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/23765
Collection计算数学与科学工程计算研究所
AffiliationChinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci & Engn Comp, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Chen, Chuchu,Hong, Jialin. SYMPLECTIC RUNGE-KUTTA SEMIDISCRETIZATION FOR STOCHASTIC SCHRODINGER EQUATION[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2016,54(4):2569-2593.
APA Chen, Chuchu,&Hong, Jialin.(2016).SYMPLECTIC RUNGE-KUTTA SEMIDISCRETIZATION FOR STOCHASTIC SCHRODINGER EQUATION.SIAM JOURNAL ON NUMERICAL ANALYSIS,54(4),2569-2593.
MLA Chen, Chuchu,et al."SYMPLECTIC RUNGE-KUTTA SEMIDISCRETIZATION FOR STOCHASTIC SCHRODINGER EQUATION".SIAM JOURNAL ON NUMERICAL ANALYSIS 54.4(2016):2569-2593.
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