Construction of Symplectic Runge-Kutta Methods for Stochastic Hamiltonian Systems

doi:10.4208/cicp.261014.230616a

	Construction of Symplectic Runge-Kutta Methods for Stochastic Hamiltonian Systems
	Wang, Peng 1; Hong, Jialin2 ; Xu, Dongsheng 2,3
	2017
发表期刊	COMMUNICATIONS IN COMPUTATIONAL PHYSICS
ISSN	1815-2406
卷号	21 期号:1 页码:237-270
摘要	We study the construction of symplectic Runge-Kutta methods for stochastic Hamiltonian systems (SHS). Three types of systems, SHS with multiplicative noise, special separable Hamiltonians and multiple additive noise, respectively, are considered in this paper. Stochastic Runge-Kutta (SRK) methods for these systems are investigated, and the corresponding conditions for SRK methods to preserve the symplectic property are given. Based on the weak/strong order and symplectic conditions, some effective schemes are derived. In particular, using the algebraic computation, we obtained two classes of high weak order symplectic Runge-Kutta methods for SHS with a single multiplicative noise, and two classes of high strong order symplectic Runge-Kutta methods for SHS with multiple multiplicative and additive noise, respectively. The numerical case studies confirm that the symplectic methods are efficient computational tools for long-term simulations.
关键词	Stochastic differential equation Stochastic Hamiltonian system symplectic integration Runge-Kutta method order condition
DOI	10.4208/cicp.261014.230616a
语种	英语
资助项目	NSFC[91130003] ; NSFC[11101184] ; NSFC[11271151] ; NSFC[11021101] ; NSFC[11290142] ; Science Foundation for Young Scientists of Jilin Province[20130522101JH]
WOS研究方向	Physics
WOS类目	Physics, Mathematical
WOS记录号	WOS:000390196800011
出版者	GLOBAL SCIENCE 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/24380
专题	计算数学与科学工程计算研究所
通讯作者	Wang, Peng
作者单位	1.Jilin Univ, Inst Math, Changchun 130012, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci & Engn Comp, Beijing 100080, Peoples R China 3.Univ Chinese Acad Sci, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Wang, Peng,Hong, Jialin,Xu, Dongsheng. Construction of Symplectic Runge-Kutta Methods for Stochastic Hamiltonian Systems[J]. COMMUNICATIONS IN COMPUTATIONAL PHYSICS,2017,21(1):237-270.
APA	Wang, Peng,Hong, Jialin,&Xu, Dongsheng.(2017).Construction of Symplectic Runge-Kutta Methods for Stochastic Hamiltonian Systems.COMMUNICATIONS IN COMPUTATIONAL PHYSICS,21(1),237-270.
MLA	Wang, Peng,et al."Construction of Symplectic Runge-Kutta Methods for Stochastic Hamiltonian Systems".COMMUNICATIONS IN COMPUTATIONAL PHYSICS 21.1(2017):237-270.