Symplectic Runge-Kutta methods for Hamiltonian systems driven by Gaussian rough paths

doi:10.1016/j.apnum.2018.03.006

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 计算数学与科学工程计算研究所

	Symplectic Runge-Kutta methods for Hamiltonian systems driven by Gaussian rough paths
	Hong, Jialin1,2 ; Huang, Chuying 1,2; Wang, Xu 1,2
刊名	APPLIED NUMERICAL MATHEMATICS
	2018-07-01
卷号	129 页码:120-136
关键词	Rough path Hamiltonian system Symplectic Runge-Kutta method Implicit method Pathwlse convergence rate
ISSN号	0168-9274
DOI	10.1016/j.apnum.2018.03.006
英文摘要	We consider Hamiltonian systems driven by multi-dimensional Gaussian processes in rough path sense, which include fractional Brownian motions with Hurst parameter H is an element of (1/4,1/2]. We prove that the phase flow preserves the symplectic structure almost surely and this property could be inherited by symplectic Runge-Kutta methods, which are implicit methods in general. If the vector fields satisfy some smoothness and boundedness conditions, we obtain the pathwise convergence rates of Runge-Kutta methods. When vector fields are linear, we get the solvability of the midpoint scheme for skew symmetric cases, and obtain its pathwise convergence rate. Numerical experiments verify our theoretical analysis. (C) 2018 IMACS. Published by Elsevier B.V. All rights reserved.
资助项目	National Natural Science Foundation of China[91530118] ; National Natural Science Foundation of China[91130003] ; National Natural Science Foundation of China[11021101] ; National Natural Science Foundation of China[91630312] ; National Natural Science Foundation of China[11290142]
WOS研究方向	Mathematics
语种	英语
出版者	ELSEVIER SCIENCE BV
WOS记录号	WOS:000430902800008
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/30268]
专题	计算数学与科学工程计算研究所
通讯作者	Huang, Chuying
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Hong, Jialin,Huang, Chuying,Wang, Xu. Symplectic Runge-Kutta methods for Hamiltonian systems driven by Gaussian rough paths[J]. APPLIED NUMERICAL MATHEMATICS,2018,129:120-136.
APA	Hong, Jialin,Huang, Chuying,&Wang, Xu.(2018).Symplectic Runge-Kutta methods for Hamiltonian systems driven by Gaussian rough paths.APPLIED NUMERICAL MATHEMATICS,129,120-136.
MLA	Hong, Jialin,et al."Symplectic Runge-Kutta methods for Hamiltonian systems driven by Gaussian rough paths".APPLIED NUMERICAL MATHEMATICS 129(2018):120-136.