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The non-existence of symplectic multi-derivative Runge-Kutta methods

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Abstract

A sufficient condition for the symplecticness ofq-derivative Runge-Kutta methods has been derived by F. M. Lasagni. In the present note we prove that this condition can only be satisfied for methods withq≤1, i.e., for standard Runge-Kutta methods. We further show that the conditions of Lasagni are also necessary for symplecticness so that no symplectic multi-derivative Runge-Kutta method can exist.

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Authors and Affiliations

  1. Dept. de mathématiques, Université de Genève, Case postale 240, CH.1211, Genève 24, Switzerland

    E. Hairer

  2. Informatika Fakultatea, Euskal Herriko Unibertsitatea, 649 Postakutxa, 20080, San Sebastian, Spain

    A. Murua

  3. Departamento de Matemática Aplicada y Computación, Facultad de Ciencias, Universidad de Valladolid, Valladolid, Spain

    J. M. Sanz-Serna

Authors
  1. E. Hairer
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  2. A. Murua
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  3. J. M. Sanz-Serna
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Additional information

This research has been supported by project PB89-0351 (Dirección General de Investigación Científica y Técnica) and by project No. 20-32354.91 of Swiss National Science Foundation.

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Hairer, E., Murua, A. & Sanz-Serna, J.M. The non-existence of symplectic multi-derivative Runge-Kutta methods. BIT 34, 80–87 (1994). https://doi.org/10.1007/BF01935017

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  • DOI: https://doi.org/10.1007/BF01935017

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