| 一类广义Hamilton系统的辛格式 |
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| 作者姓名： | Zhao Ying Wang Bin Ji Zhongzhen |
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| 作者单位： | Zhao Ying 1，2，Wang Bin 1，and Ji Zhongzhen1LASG，Institute of Atmospheric Physics，Chinese Academy of Sciences，Beijing 100029 2Institute of Science，PLA University of Science and Technology，Nanjing 211101 |
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| 基金项目： | Acknowledgments. This work was supported by the China National Key Development Planning Project for Ba-sic Research (Abbreviation: 973 Project，Grant No. G1999032801), the Chinese Academy of Sciences Key Innovation Direction Project (Grant No. KZCX2208) |
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| 摘 要： | 通过引人泊松括号，分析了无限维Hamilton的性质，并将其推广到广义Hamilton系统，且从理论和实用角度讨论了这类广义Hamilton系统的辛格式构造问题，从而为辛几何算法在一般的时间发展方程的数值求解提供新的具体途径。
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| 关 键 词： | 无限维Hamilton系统 广义Hamilton系统 辛格式 泊松括号 辛几何算法 时间发展方程 数值求解 |
| 收稿时间： | 20 June 2001 |
Symplectic-like difference schemes for generalized hamiltonian systems |
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| Zhao Ying,Wang Bin,Ji Zhongzhen.Symplectic-like difference schemes for generalized hamiltonian systems[J].Advances in Atmospheric Sciences,2002,19(4):719-726. |
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| Authors: | Zhao Ying Wang Bin Ji Zhongzhen |
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| Institution: | 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 |
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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. |
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| Keywords: | infinite-dimensional Hamiltonian systems generalized Hamiltonian systems symplectic-like difference schemes Poisson brackets |
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