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

  • Regular Article - Theoretical Physics
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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.

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Notes

  1. As an exceptional case, FR has fourth-order accuracy when H 1 is solved analytically by Eq. (3).

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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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Authors and Affiliations

  1. School of Science, Nanchang University, Nanchang, 330031, China

    Lijie Mei & Xin Wu

  2. Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing, 210008, China

    Xin Wu

  3. School of Mathematics and Information, Shanghai Lixin University of Commerce, Shanghai, 201600, China

    Fuyao Liu

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  1. Lijie Mei
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  2. Xin Wu
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  3. Fuyao Liu
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Correspondence to Xin Wu.

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Mei, L., Wu, X. & Liu, F. On preference of Yoshida construction over Forest–Ruth fourth-order symplectic algorithm. Eur. Phys. J. C 73, 2413 (2013). https://doi.org/10.1140/epjc/s10052-013-2413-y

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