Year: 1989
Author: Kang Feng, Hua-Mo Wu, Meng-Zhao Qin, Dao-Liu Wang
Journal of Computational Mathematics, Vol. 7 (1989), Iss. 1 : pp. 71–96
Abstract
This paper discusses the relationship between canonical maps and generating functions and gives the general Hamilton-Jacobi theory for time-independent Hamiltonian systems. Based on this theory, the general method — the generating function method — of the construction of difference schemes for Hamiltonian systems is considered. The transition of such difference schemes from one time-step to the next is canonical. So they are called the canonical difference schemes. The well known Euler centered scheme is a canonical difference scheme. Its higher order canonical generalisations and other families of canonical difference schemes are given. The construction method proposed in the paper is also applicable to time-dependent Hamiltonian systems.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1989-JCM-9457
Journal of Computational Mathematics, Vol. 7 (1989), Iss. 1 : pp. 71–96
Published online: 1989-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 26