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A G-symplectic method with order 6

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Abstract

G-symplectic methods are an alternative to symplectic Runge–Kutta in that they have similar numerical behaviour but are less expensive computationally. In this paper, a new method is derived which is symmetric, G-symplectic, has zero parasitic growth factors and has order 6. Although there are five stages, two of these are explicit and the remaining three are diagonally implicit. The method is multivalue, with four quantities passed from step to step. No drift in the variation of the Hamiltonian is observed in numerical experiments for long time intervals if the stepsize is sufficiently small.

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Acknowledgments

The authors gratefully acknowledge the constructive comments of the associate editor and the anonymous referees. Funding was provided by Marsden Fund (AMC1101).

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Authors and Affiliations

  1. Department of Mathematics, University of Auckland, Auckland, New Zealand

    John C. Butcher & Gulshad Imran

  2. Institute for Mathematics, Martin Luther University Halle-Wittenberg, Theodor Lieser Str 5, 06120, Halle, Germany

    Helmut Podhaisky

Authors
  1. John C. Butcher
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  2. Gulshad Imran
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  3. Helmut Podhaisky
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Correspondence to John C. Butcher.

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Communicated by David Cohen.

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Butcher, J.C., Imran, G. & Podhaisky, H. A G-symplectic method with order 6. Bit Numer Math 57, 313–328 (2017). https://doi.org/10.1007/s10543-016-0630-0

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  • DOI: https://doi.org/10.1007/s10543-016-0630-0

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