Volume 9, Issue 2
Poisson Difference Schemes for Hamiltonian Systems on Poisson Manifolds

Dao-liu Wang

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J. Comp. Math., 9 (1991), pp. 115-124

Published online: 1991-09

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  • Abstract

In this paper a systematical method for the construction of Poisson difference schemes with arbitrary order of accuracy for Hamiltonian systems on Poisson manifolds is considered. The transition of such difference schemes from one time-step to the next is a Poisson map. In addition, these schemes preserve all Casimir functions and, under certain conditions, quadratic first integrals of the original Hamiltonian systems. Especially, the arbitrary order centered schemes preserve all Casimir functions and all quadratic first integrals of the original Hamiltonian systems.

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@Article{JCM-9-115, author = {}, title = {Poisson Difference Schemes for Hamiltonian Systems on Poisson Manifolds}, journal = {Journal of Computational Mathematics}, year = {1991}, volume = {9}, number = {2}, pages = {115--124}, abstract = { In this paper a systematical method for the construction of Poisson difference schemes with arbitrary order of accuracy for Hamiltonian systems on Poisson manifolds is considered. The transition of such difference schemes from one time-step to the next is a Poisson map. In addition, these schemes preserve all Casimir functions and, under certain conditions, quadratic first integrals of the original Hamiltonian systems. Especially, the arbitrary order centered schemes preserve all Casimir functions and all quadratic first integrals of the original Hamiltonian systems. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9384.html} }
TY - JOUR T1 - Poisson Difference Schemes for Hamiltonian Systems on Poisson Manifolds JO - Journal of Computational Mathematics VL - 2 SP - 115 EP - 124 PY - 1991 DA - 1991/09 SN - 9 DO - http://dor.org/ UR - https://global-sci.org/intro/jcm/9384.html KW - AB - In this paper a systematical method for the construction of Poisson difference schemes with arbitrary order of accuracy for Hamiltonian systems on Poisson manifolds is considered. The transition of such difference schemes from one time-step to the next is a Poisson map. In addition, these schemes preserve all Casimir functions and, under certain conditions, quadratic first integrals of the original Hamiltonian systems. Especially, the arbitrary order centered schemes preserve all Casimir functions and all quadratic first integrals of the original Hamiltonian systems.
Dao-liu Wang. (1970). Poisson Difference Schemes for Hamiltonian Systems on Poisson Manifolds. Journal of Computational Mathematics. 9 (2). 115-124. doi:
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