SYMPLECTIC RUNGE-KUTTA SEMIDISCRETIZATION FOR STOCHASTIC SCHRODINGER EQUATION

doi:10.1137/151005208

	SYMPLECTIC RUNGE-KUTTA SEMIDISCRETIZATION FOR STOCHASTIC SCHRODINGER EQUATION
	Chen, Chuchu; Hong, Jialin
	2016
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	54 期号:4 页码:2569-2593
摘要	Based 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.
关键词	stochastic Schrodinger equation infinite-dimensional stochastic Hamiltonian system symplectic structure symplectic Runge-Kutta method semidiscretization mean-square convergence order
DOI	10.1137/151005208
语种	英语
资助项目	National Natural Science Foundation of China[91130003] ; National Natural Science Foundation of China[11021101] ; National Natural Science Foundation of China[11290142]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000385274300024
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/23765
专题	计算数学与科学工程计算研究所
通讯作者	Chen, Chuchu
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci & Engn Comp, Beijing 100190, Peoples R China
推荐引用方式 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.