TY - JOUR
T1 - High-Order Symplectic and Symmetric Composition Methods for Multi-Frequency and Multi-Dimensional Oscillatory Hamiltonian Systems
AU - Liu , Kai
AU - Wu , Xinyuan
JO - Journal of Computational Mathematics
VL - 4
SP - 356
EP - 378
PY - 2015
DA - 2015/08
SN - 33
DO - http://doi.org/10.4208/jcm.1502-m2014-0082
UR - https://global-sci.org/intro/article_detail/jcm/9848.html
KW - Symplectic and symmetric composition methods, Multi-frequency and multi-dimensional ERKN integrators, ARKN integrators, Multi-frequency oscillatory Hamiltonian systems.
AB - <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>