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

作　　者：胡妹芳 陈传淼 

机构地区：[1]College of Mathematics and Computer Science, Hunan Normal University [2]Institute of Mathematics and Physics, Central South University of Forestry and Technology

出　　处：《Applied Mathematics and Mechanics(English Edition)》2013年第6期747-760,共14页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (No. 11071067);the Hunan Graduate Student Science and Technology Innovation Project (No. CX2011B184)

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.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.

关 键 词：Hamiltonian system energy conservation SYMPLECTICITY finite elementmethod Runge-Kutta method 

分 类 号：O241.82[理学—计算数学]