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Generating Function Methods for Coefficient-Varying Generalized Hamiltonian Systems

Published online by Cambridge University Press:  03 June 2015

Xueyang Li ,
Aiguo Xiao  and
Dongling Wang
Xueyang Li*
Affiliation:
Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University, Xiangtan 411105, Hunan, China
Aiguo Xiao
Affiliation:
Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University, Xiangtan 411105, Hunan, China
Dongling Wang
Affiliation:
Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University, Xiangtan 411105, Hunan, China
*
*Corresponding author. Email: lixy1217@163.com
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Abstract

The generating function methods have been applied successfully to generalized Hamiltonian systems with constant or invertible Poisson-structure matrices. In this paper, we extend these results and present the generating function methods preserving the Poisson structures for generalized Hamiltonian systems with general variable Poisson-structure matrices. In particular, some obtained Poisson schemes are applied efficiently to some dynamical systems which can be written into generalized Hamiltonian systems (such as generalized Lotka-Volterra systems, Robbins equations and so on).

Keywords

65P1065L0537M1570H05Generalized Hamiltonian systemsPoisson manifoldsgenerating functionsstructure preserving algorithmsgeneralized Lotka-Volterra systems
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 6 , Issue 1 , February 2014 , pp. 87 - 106
Copyright
Copyright © Global-Science Press 2014

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