KMS Of Academy of mathematics and systems sciences, CAS
| Variations on a theme by Euler | |
| Feng, K; Wang, DL | |
| 1998-03-01 | |
| Source Publication | JOURNAL OF COMPUTATIONAL MATHEMATICS
 |
| ISSN | 0254-9409 |
| Volume | 16Issue:2Pages:97-106 |
| Abstract | 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. |
| Keyword | Hamiltonian systems symplectic difference schemes explicit Euler method nilpotent symplectically separable |
| Language | 英语 |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied ; Mathematics |
| WOS ID | WOS:000072568700001 |
| Publisher | VSP BV |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/13665 |
| Collection | 中国科学院数学与系统科学研究院 |
| Affiliation | Chinese 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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