|
|||||
|
|
| 哈密尔顿系统的有限元法 | |
| 引用本文： | 汤琼,陈传淼,刘罗华.哈密尔顿系统的有限元法[J].计算数学,2009,31(4):393-406. |
| 作者姓名： | 汤琼 陈传淼 刘罗华 |
| 作者单位： | 1. 湖南工业大学理学院,湖南株洲,412008 2. 湖南师范大学数学与计算机科学学院,长沙,410081 |
| 基金项目： | 国家自然科学基金，湖南省自然科学基金资助项目 |
| 摘 要： | 利用常微分方程的连续有限元法,结合函数的M-型展开,对非线性哈密尔顿系统证明了连续一、二次有限元分在3阶量、5阶量意义下近似保辛,且保持能量守恒.在数值实验中结合庞加莱截面,哈密尔顿混沌数值试验结果与理论相吻合. |
| 关 键 词： | 哈密尔顿方程 连续有限元方法 辛算法 能量守恒 混沌 |
| 收稿时间： | 2008-09-08 |
FINITE ELEMENT METHODS FOR HAMILTONIAN SYSTEMS |
|
| Tang Qiong,Chen Chuanmiao,Liu Luohua.FINITE ELEMENT METHODS FOR HAMILTONIAN SYSTEMS[J].Mathematica Numerica Sinica,2009,31(4):393-406. | |
| Authors: | Tang Qiong Chen Chuanmiao Liu Luohua |
| Institution: | 1. College of Science, Hunan University of Technology, Hunan, Zhuzhou 412008, China; 2. Department of Mathematics and Computer Science, Hunan Normal University, Hunan, Changsha 410081, China; 3. College of Science, Hunan University of Technology, Hunan, Zhuzhou 412008, China |
| Abstract: | By applying the continuous finite element methods for ordinary differential equations and combine M-type function unfold, the linear element are proved an approximately symplectic method which is accurate of third order to their symplectic structure and the quadratic element are proved an approximately symplectic method which is accurate of fifth order to their symplectic structure, as well as energy conservative. Combine Poincarê section, the numerical results of Hamiltonian chaos agree with the theory. |
| Keywords: | Hamiltonian systems continuous finite element method symplectic algorithm energy conservation chaos |
| 本文献已被 万方数据 等数据库收录！ | |
| 点击此处可从《计算数学》浏览原始摘要信息 | |
| 点击此处可从《计算数学》下载免费的PDF全文 | |