Variations on a theme by Euler

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	Variations on a theme by Euler
	Feng, K; Wang, DL
	1998-03-01
发表期刊	JOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN	0254-9409
卷号	16 期号:2 页码:97-106
摘要	The oldest and simplest difference scheme is the explicit Euler method. Usually, it is not symplectic for general Hamiltonian systems. It is interesting to ask: Under what conditions of Hamiltonians, the explicit Euler method becomes symplectic? In this paper, we give the class of Hamiltonians for which systems the explicit Euler method is symplectic. In fact, in these cases, the explicit Euler method is really the phase how of the systems, therefore symplectic. Most of important Hamiltonian systems can be decomposed as the summation of these simple systems. Then composition of the Euler method acting on these systems yields a symplectic method, also explicit. These systems are called symplectically separable. Classical separable Hamiltonian systems are symplectically separable. Especially, we prove that any polynomial Hamiltonian is symplectically separable.
关键词	Hamiltonian systems symplectic difference schemes explicit Euler method nilpotent symplectically separable
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000072568700001
出版者	VSP BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/13665
专题	中国科学院数学与系统科学研究院
作者单位	Chinese Acad Sci, ICMSEC, State Key Lab Sci & Engn Comp, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Feng, K,Wang, DL. Variations on a theme by Euler[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS,1998,16(2):97-106.
APA	Feng, K,&Wang, DL.(1998).Variations on a theme by Euler.JOURNAL OF COMPUTATIONAL MATHEMATICS,16(2),97-106.
MLA	Feng, K,et al."Variations on a theme by Euler".JOURNAL OF COMPUTATIONAL MATHEMATICS 16.2(1998):97-106.