Variations on a theme by Euler
Feng, K; Wang, DL
AbstractThe 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.
KeywordHamiltonian systems symplectic difference schemes explicit Euler method nilpotent symplectically separable
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000072568700001
PublisherVSP BV
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Document Type期刊论文
AffiliationChinese Acad Sci, ICMSEC, State Key Lab Sci & Engn Comp, Beijing 100080, Peoples R China
Recommended Citation
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.
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