@Article{JCM-33-4,
author = {Liu, Kai and Xinyuan, Wu},
title = {High-Order Symplectic and Symmetric Composition Methods for Multi-Frequency and Multi-Dimensional Oscillatory Hamiltonian Systems},
journal = {Journal of Computational Mathematics},
year = {2015},
volume = {33},
number = {4},
pages = {356--378},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1502-m2014-0082},
url = {https://global-sci.com/article/84604/high-order-symplectic-and-symmetric-composition-methods-for-multi-frequency-and-multi-dimensional-oscillatory-hamiltonian-systems}
}