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.
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 Poincare section, the numerical results of Hamiltonian chaos agree with the theory.
出处
《计算数学》
CSCD
北大核心
2009年第4期393-406,共14页
Mathematica Numerica Sinica
基金
国家自然科学基金(10771063
60874025)
湖南省自然科学基金资助项目(09JJ3007)资助项目
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
Hamiltonian systems
continuous finite element method
symplectic algorithm
energy conservation
chaos
