A symplectic structure preserved by the trapezoidal rule

doi:10.1143/JPSJ.72.2193

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	A symplectic structure preserved by the trapezoidal rule
	Tam, HW ; Wang, DL
	2003-09-01
发表期刊	JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN
ISSN	0031-9015
卷号	72 期号:9 页码:2193-2197
摘要	The 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)).
关键词	symplectic structure trapezoidal rule Richardson's extrapolation
DOI	10.1143/JPSJ.72.2193
语种	英语
WOS研究方向	Physics
WOS类目	Physics, Multidisciplinary
WOS记录号	WOS:000185540600015
出版者	PHYSICAL SOC JAPAN
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/18641
专题	中国科学院数学与系统科学研究院
通讯作者	Tam, HW
作者单位	1.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
推荐引用方式 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.