High-Order Symplectic and Symmetric Composition Methods for Multi-Frequency and Multi-Dimensional Oscillatory Hamiltonian Systems
Year: 2015
Author: Kai Liu, Xinyuan Wu
Journal of Computational Mathematics, Vol. 33 (2015), Iss. 4 : pp. 356–378
Abstract
The multi-frequency and multi-dimensional adapted Runge-Kutta-Nyström (ARKN) integrators, and multi-frequency and multi-dimensional extended Runge-Kutta-Nyström(ERKN) integrators have been developed to efficiently solve multi-frequency oscillatory Hamiltonian systems. The aim of this paper is to analyze and derive high-order symplectic and symmetric composition methods based on the ARKN integrators and ERKN integrators. We first consider the symplecticity conditions for the multi-frequency and multi-dimensional ARKN integrators. We then analyze the symplecticity of the adjoint integrators of the multi-frequency and multi-dimensional symplectic ARKN integrators and ERKN integrators, respectively. On the basis of the theoretical analysis and by using the idea of composition methods, we derive and propose four new high-order symplectic and symmetric methods for the multi-frequency oscillatory Hamiltonian systems. The numerical results accompanied in this paper quantitatively show the advantage and efficiency of the proposed high-order symplectic and symmetric methods.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1502-m2014-0082
Journal of Computational Mathematics, Vol. 33 (2015), Iss. 4 : pp. 356–378
Published online: 2015-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Symplectic and symmetric composition methods Multi-frequency and multi-dimensional ERKN integrators ARKN integrators Multi-frequency oscillatory Hamiltonian systems.
Author Details
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