@Article{JCM-7-1,
author = {Kang, Feng and Wu, Hua-Mo and Qin, Meng-Zhao and Wang, Dao-Liu},
title = {Construction of Canonical Difference Schemes for Hamiltonian Formalism via Generating Functions},
journal = {Journal of Computational Mathematics},
year = {1989},
volume = {7},
number = {1},
pages = {71--96},
abstract = {<p style="text-align: justify;">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. &nbsp;</p>},
issn = {1991-7139},
doi = {https://doi.org/1989-JCM-9457},
url = {https://global-sci.com/article/86083/construction-of-canonical-difference-schemes-for-hamiltonian-formalism-via-generating-functions}
}