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Stochastic symplectic Runge-Kutta methods for the strong approximation of Hamiltonian systems with additive noise
Zhou, Weien1; Zhang, Jingjing3; Hong, Jialin4; Song, Songhe1,2
2017-12-01
Source PublicationJOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN0377-0427
Volume325Pages:134-148
AbstractIn this paper, we construct stochastic symplectic Runge Kutta (SSRK) methods of high strong order for Hamiltonian systems with additive noise. By means of colored rooted tree theory, we combine conditions of mean-square order 1.5 and symplectic conditions to get totally derivative free schemes. We also achieve mean-square order 2.0 symplectic schemes for a class of second-order Hamiltonian systems with additive noise by similar analysis. Finally, linear and non-linear systems are solved numerically, which verifies the theoretical analysis on convergence order. Especially for the stochastic harmonic oscillator with additive noise, the linear growth property can be preserved exactly over long-time simulation. (C) 2017 Elsevier B.V. All rights reserved.
KeywordStochastic differential equations Stochastic Runge-Kutta methods Symplectic integrators Mean-square convergence
DOI10.1016/j.cam.2017.04.050
Language英语
Funding ProjectHPCL ; NSFC[11501570] ; NSFC[11571366] ; NSFC[11201125] ; NSFC[91130003] ; NSFC[11021101] ; NSFC[11290142] ; NSFC[91530018] ; foundation of department of education of Henan province[12B110010] ; young growth foundation of Henan Polytechnic university[B2390]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000404308000010
PublisherELSEVIER SCIENCE BV
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/25815
Collection计算数学与科学工程计算研究所
Affiliation1.Natl Univ Def Technol, Coll Sci, Changsha 410073, Hunan, Peoples R China
2.Natl Univ Def Technol, State Key Lab High Performance Comp, Changsha 410073, Hunan, Peoples R China
3.East China Jiaotong Univ, Sch Sci, Nanchang 330013, Jiangxi, Peoples R China
4.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Zhou, Weien,Zhang, Jingjing,Hong, Jialin,et al. Stochastic symplectic Runge-Kutta methods for the strong approximation of Hamiltonian systems with additive noise[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2017,325:134-148.
APA Zhou, Weien,Zhang, Jingjing,Hong, Jialin,&Song, Songhe.(2017).Stochastic symplectic Runge-Kutta methods for the strong approximation of Hamiltonian systems with additive noise.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,325,134-148.
MLA Zhou, Weien,et al."Stochastic symplectic Runge-Kutta methods for the strong approximation of Hamiltonian systems with additive noise".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 325(2017):134-148.
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