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A symplectic structure preserved by the trapezoidal rule
Tam, HW; Wang, DL
2003-09-01
Source PublicationJOURNAL OF THE PHYSICAL SOCIETY OF JAPAN
ISSN0031-9015
Volume72Issue:9Pages:2193-2197
AbstractThe trapezoidal rule has often been referred to as being symmetric or time-reversible and is therefore good for Hamiltonian systems. However, it is well-known that the trapezoidal rule is not symplectic, but is related to the mid-point rule (which is symplectic) through a coordinate transformation. In this paper, we show that the trapezoidal rule preserves a symplectic structure different from the original one by O(h(2)). The ideas in this paper also motivate us to apply Richardson's extrapolation to the trapezoidal rule. Numerical results show that the extrapolated trapezoidal rule preserves the Hamiltonian up to O(h(4)).
Keywordsymplectic structure trapezoidal rule Richardson's extrapolation
DOI10.1143/JPSJ.72.2193
Language英语
WOS Research AreaPhysics
WOS SubjectPhysics, Multidisciplinary
WOS IDWOS:000185540600015
PublisherPHYSICAL SOC JAPAN
Citation statistics
Cited Times:4[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/18641
Collection中国科学院数学与系统科学研究院
Affiliation1.Hong Kong Baptist Univ, Dept Comp Sci, Kowloon, Hong Kong, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Sci & Engn Comp, Inst Computat Math & Sci Engn Comp, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
Tam, HW,Wang, DL. A symplectic structure preserved by the trapezoidal rule[J]. JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN,2003,72(9):2193-2197.
APA Tam, HW,&Wang, DL.(2003).A symplectic structure preserved by the trapezoidal rule.JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN,72(9),2193-2197.
MLA Tam, HW,et al."A symplectic structure preserved by the trapezoidal rule".JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 72.9(2003):2193-2197.
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