BIT Numerical Mathematics

, Volume 34, Issue 1, pp 80–87 | Cite as

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

  • E. Hairer
  • A. Murua
  • J. M. Sanz-Serna


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.

AMS subject classification

65L06 70H15 

Key words

Multi-derivative Runge-Kutta methods symplectic methods irreducible methods 


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Copyright information

© the BIT Foundation 1994

Authors and Affiliations

  • E. Hairer
    • 1
  • A. Murua
    • 2
  • J. M. Sanz-Serna
    • 3
  1. 1.Dept. de mathématiquesUniversité de GenèveGenève 24Switzerland
  2. 2.Informatika FakultateaEuskal Herriko UnibertsitateaSan SebastianSpain
  3. 3.Departamento de Matemática Aplicada y Computación, Facultad de CienciasUniversidad de ValladolidValladolidSpain

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