CSpace  > 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, Chuying1,2; Wang, Xu1,2
2018-07-01
Source PublicationAPPLIED NUMERICAL MATHEMATICS
ISSN0168-9274
Volume129Pages:120-136
AbstractWe 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.
KeywordRough path Hamiltonian system Symplectic Runge-Kutta method Implicit method Pathwlse convergence rate
DOI10.1016/j.apnum.2018.03.006
Language英语
Funding ProjectNational 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 Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000430902800008
PublisherELSEVIER SCIENCE BV
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/30269
Collection计算数学与科学工程计算研究所
Affiliation1.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
Recommended Citation
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.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Bookmark
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[Hong, Jialin]'s Articles
[Huang, Chuying]'s Articles
[Wang, Xu]'s Articles
Baidu academic
Similar articles in Baidu academic
[Hong, Jialin]'s Articles
[Huang, Chuying]'s Articles
[Wang, Xu]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Hong, Jialin]'s Articles
[Huang, Chuying]'s Articles
[Wang, Xu]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.
 

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.