https://doi.org/10.1140/epjc/s10052-013-2413-y
Regular Article - Theoretical Physics
On preference of Yoshida construction over Forest–Ruth fourth-order symplectic algorithm
1
School of Science, Nanchang University, Nanchang, 330031, China
2
Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing, 210008, China
3
School of Mathematics and Information, Shanghai Lixin University of Commerce, Shanghai, 201600, China
* e-mail: xwu@ncu.edu.cn
Received:
10
December
2012
Revised:
26
March
2013
Published online:
8
May
2013
The Forest–Ruth fourth-order symplectic algorithm is identical to the Yoshida triplet construction when all component integrators of both algorithms are exactly known. However, this equality no longer holds in general when some or all of the components are inexact and when they are second-order with odd-order error structures. The former algorithm is only second-order accurate in most cases, whereas the latter can be fourth-order accurate. These analytical results are supported by numerical simulations of partially separable but globally inseparable Hamiltonian systems, such as the post-Newtonian Hamiltonian formulation of spinless compact binaries. Therefore, the Yoshida construction has intrinsic merit over the concatenated Forest–Ruth algorithm when inexact component integrators are used.
© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica, 2013
