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Volume 7, Issue 1
Construction of Canonical Difference Schemes for Hamiltonian Formalism via Generating Functions

Kang Feng, Hua-Mo Wu, Meng-Zhao Qin & Dao-Liu Wang

J. Comp. Math., 7 (1989), pp. 71-96.

Published online: 1989-07

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  • 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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@Article{JCM-7-71, author = {Feng , KangWu , Hua-MoQin , 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 = {

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.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9457.html} }
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 -

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.  

Kang Feng, Hua-Mo Wu, Meng-Zhao Qin & Dao-Liu Wang. (1970). Construction of Canonical Difference Schemes for Hamiltonian Formalism via Generating Functions. Journal of Computational Mathematics. 7 (1). 71-96. doi:
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