The Continuous Finite Element Methods for a Simple Case of Separable Hamiltonian Systems
Applied and Computational Mathematics
Volume 4, Issue 2, April 2015, Pages: 39-46
Received: Dec. 22, 2014; Accepted: Feb. 6, 2015; Published: Mar. 6, 2015
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Authors
Qiong Tang, College of Science, Hunan University of Technology, Zhuzhou, Hunan, P.R. China
Luohua Liua, College of Science, Hunan University of Technology, Zhuzhou, Hunan, P.R. China
Yujun Zheng, Department of mathematics and Computational Science, Hunan University of Science and Engineering, YongZhou, Hunan, P.R. China
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Abstract
Combined with the characteristics of separable Hamiltonian systems and the finite element methods of ordinary differential equations, we prove that the composition of linear, quadratic, cubic finite element methods are symplectic integrator to separable Hamiltonian systems, i.e. the symplectic condition is preserved exactly, but the energy is only approximately conservative after compound. These conclusions are confirmed by our numerical experiments.
Keywords
Separable Hamiltonian Systems, Finite Element Methods, Composition Methods, Symplectic Integrator
To cite this article
Qiong Tang, Luohua Liua, Yujun Zheng, The Continuous Finite Element Methods for a Simple Case of Separable Hamiltonian Systems, Applied and Computational Mathematics. Vol. 4, No. 2, 2015, pp. 39-46. doi: 10.11648/j.acm.20150402.12
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