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线性Hamilton系统边值问题的保辛数值方法

蒋宪宏 邓子辰 张凯 王嘉琪

蒋宪宏, 邓子辰, 张凯, 王嘉琪. 线性Hamilton系统边值问题的保辛数值方法[J]. 应用数学和力学, 2017, 38(9): 988-998. doi: 10.21656/1000-0887.370365
引用本文: 蒋宪宏, 邓子辰, 张凯, 王嘉琪. 线性Hamilton系统边值问题的保辛数值方法[J]. 应用数学和力学, 2017, 38(9): 988-998. doi: 10.21656/1000-0887.370365
JIANG Xian-hong, DENG Zi-chen, ZHANG Kai, WANG Jia-qi. A Symplectic Approach for Boundary-Value Problems of Linear Hamiltonian Systems[J]. Applied Mathematics and Mechanics, 2017, 38(9): 988-998. doi: 10.21656/1000-0887.370365
Citation: JIANG Xian-hong, DENG Zi-chen, ZHANG Kai, WANG Jia-qi. A Symplectic Approach for Boundary-Value Problems of Linear Hamiltonian Systems[J]. Applied Mathematics and Mechanics, 2017, 38(9): 988-998. doi: 10.21656/1000-0887.370365

线性Hamilton系统边值问题的保辛数值方法

doi: 10.21656/1000-0887.370365
基金项目: 国家自然科学基金(11432010)
详细信息
    作者简介:

    蒋宪宏(1991—),男,硕士生(E-mail: Jhonstarx@mail.nwpu.edu.cn);邓子辰(1964—),男,教授,博士生导师(通讯作者. E-mail: dweifan@nwpu.edu.cn).

  • 中图分类号: O302; O241

A Symplectic Approach for Boundary-Value Problems of Linear Hamiltonian Systems

Funds: The National Natural Science Foundation of China(11432010)
  • 摘要: 以Hamilton系统的正则变换和生成函数为基础研究线性时变Hamilton系统边值问题的保辛数值求解算法.根据第二类生成函数系数矩阵与状态传递矩阵的关系,构造了生成函数系数矩阵的区段合并递推算法,并进一步将递推算法推广到线性非齐次边值问题中;然后利用生成函数的性质将边值问题转化为初值问题,最后采用初值问题的保辛算法求解以达到整个Hamilton系统保辛的目的.数值算例表明该方法能够有效地求解线性齐次与非齐次问题,并能很好地保持Hamilton系统的固有特性.
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出版历程
  • 收稿日期:  2016-11-24
  • 修回日期:  2017-06-20
  • 刊出日期:  2017-09-15

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