Year: 1998
Author: Kang Feng, Daoliu Wang
Journal of Computational Mathematics, Vol. 16 (1998), Iss. 2 : pp. 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 flow 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1998-JCM-9144
Journal of Computational Mathematics, Vol. 16 (1998), Iss. 2 : pp. 97–106
Published online: 1998-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: Hamiltonian systems symplectic difference schemes explicit Euler method nilpotent symplectically separable.