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Preservation of equilibria for symplectic methods applied to Hamiltonian systems

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Abstract

In this paper, the linear stability of symplectic methods for Hamiltonian systems is studied. In particular, three classes of symplectic methods are considered: symplectic Runge-Kutta (SRK) methods, symplectic partitioned Runge-Kutta (SPRK) methods and the composition methods based on SRK or SPRK methods. It is shown that the SRK methods and their compositions preserve the ellipticity of equilibrium points unconditionally, whereas the SPRK methods and their compositions have some restrictions on the time-step.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Hebei University of Economics & Business, Shijiazhuang, 050061, China

    Ling-shu Wang

  2. School of Science, Tianjin University of Commerce, Tianjin, 300134, China

    Ying Wang

Authors
  1. Ling-shu Wang
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  2. Ying Wang
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Correspondence to Ling-shu Wang.

Additional information

Supported by the National Natural Science Foundation of China (No. 10926064, 10571173) and the Scientific Research Foundation of Hebei Education Department (No. 2009114).

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Wang, Ls., Wang, Y. Preservation of equilibria for symplectic methods applied to Hamiltonian systems. Acta Math. Appl. Sin. Engl. Ser. 26, 219–228 (2010). https://doi.org/10.1007/s10255-009-7145-2

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  • DOI: https://doi.org/10.1007/s10255-009-7145-2

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