Symplectic-like Difference Schemes for Generalized Hamiltonian Systems

Zhao Ying; Wang Bin; Ji Zhongzhen

doi:10.1007/s00376-002-0011-2

Impact Factor: 5.8

Volume 19 Issue 4

Jul. 2002

Article Contents

Article > ADVANCES IN ATMOSPHERIC SCIENCES > 2002 > 19(4): 719-726

Symplectic-like Difference Schemes for Generalized Hamiltonian Systems

1.
LASG, Inslilute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029;Institute of Science, PLA University of Science and Technology, Nanjing 211101,LASG, Inslilute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,LASG, Inslilute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029

doi: 10.1007/s00376-002-0011-2

Abstract
References
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Abstract:
The nature of infinite-dimensional Hamiltonian systems are studied for the purpose of further study on some generalized Hamiltonian systems equipped with a given Poisson bracket. From both theoretical and practical viewpoints, we summarize a general method of constructing symplectic-like difference schemes of these kinds of systems. This study provides a new algorithm for the application of the symplectic geometry method in numerical solutions of general evolution equations.
- infinite-dimensional Hamiltonian systems,
- generalized Hamiltonian systems,
- symplectic-like difference schemes,
- Poisson brackets
References

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Manuscript History

Manuscript received: 10 July 2002

Manuscript revised: 10 July 2002

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Symplectic-like Difference Schemes for Generalized Hamiltonian Systems

1. LASG, Inslilute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029;Institute of Science, PLA University of Science and Technology, Nanjing 211101,LASG, Inslilute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,LASG, Inslilute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029

Manuscript received: 2002-07-10
Manuscript revised: 2002-07-10

Abstract: The nature of infinite-dimensional Hamiltonian systems are studied for the purpose of further study on some generalized Hamiltonian systems equipped with a given Poisson bracket. From both theoretical and practical viewpoints, we summarize a general method of constructing symplectic-like difference schemes of these kinds of systems. This study provides a new algorithm for the application of the symplectic geometry method in numerical solutions of general evolution equations.

Keywords: