Runge-kutta method, finite element method, and regular algorithms for hamiltonian system |
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Authors: | Shu-fang Hu Chuan-miao Chen |
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Institution: | 1. College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, P. R. China;
2. Institute of Mathematics and Physics, Central South University of Forestry and Technology, Changsha 410004, P. R. China |
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Abstract: | The symplectic algorithm and the energy conservation algorithm are two important kinds of algorithms to solve Hamiltonian systems. The symplectic RungeKutta (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. |
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Keywords: | Hamiltonian system energy conservation symplecticity finite elementmethod Runge-Kutta method |
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