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On preference of Yoshida construction over Forest–Ruth fourth-order symplectic algorithm

  • Lijie Mei
  • Xin WuEmail author
  • Fuyao Liu
Regular Article - Theoretical Physics

Abstract

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.

Keywords

Energy Error Symplectic Integrator Symplectic Method Compact Binary Symmetric Composition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

We are very grateful to a referee for true comments and useful suggestions. This research is supported by the Natural Science Foundation of China under Grant Nos. 11173012, 11178002 and 11178014.

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Copyright information

© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2013

Authors and Affiliations

  1. 1.School of ScienceNanchang UniversityNanchangChina
  2. 2.Purple Mountain ObservatoryChinese Academy of SciencesNanjingChina
  3. 3.School of Mathematics and InformationShanghai Lixin University of CommerceShanghaiChina

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