TY - JOUR
T1 - Construction of Canonical Difference Schemes for Hamiltonian Formalism via Generating Functions
AU - Feng , Kang
AU - Wu , Hua-Mo
AU - Qin , Meng-Zhao
AU - Wang , Dao-Liu
JO - Journal of Computational Mathematics
VL - 1
SP - 71
EP - 96
PY - 1989
DA - 1989/07
SN - 7
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/9457.html
KW - 
AB - <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>