TY - JOUR
T1 - Poisson Difference Schemes for Hamiltonian Systems on Poisson Manifolds
AU - Wang , Dao-Liu
JO - Journal of Computational Mathematics
VL - 2
SP - 115
EP - 124
PY - 1991
DA - 1991/09
SN - 9
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/9384.html
KW - 
AB - <p style="text-align: justify;">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.</p>