Runge-Kutta method, finite element method, and regular algorithms for Hamiltonian system

被引:3
作者
胡妹芳 [1 ,2 ]
陈传淼 [1 ]
机构
[1] College of Mathematics and Computer Science, Hunan Normal University
[2] Institute of Mathematics and Physics, Central South University of Forestry and Technology
基金
中国国家自然科学基金;
关键词
Hamiltonian system; energy conservation; symplecticity; finite element method; Runge-Kutta method;
D O I
暂无
中图分类号
O241.82 [偏微分方程的数值解法];
学科分类号
070102 ;
摘要
The symplectic algorithm and the energy conservation algorithm are two important kinds of algorithms to solve Hamiltonian systems. The symplectic Runge-Kutta (RK) method is an important part of the former, and the continuous finite element method (CFEM) belongs to the later. We find and prove the equivalence of one kind of the implicit RK method and the CFEM, give the coefficient table of the CFEM to simplify its computation, propose a new standard to measure algorithms for Hamiltonian systems, and define another class of algorithms-the regular method. Finally, numerical experiments are given to verify the theoretical results.
引用
收藏
页码:747 / 760
页数:14
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