The existence of symplectic general linear methods

J C Butcher, Laura L Hewitt

Research output: Contribution to journalArticlepeer-review

13 Citations (SciVal)


We derive a criterion that any general linear method must satisfy if it is symplectic. It is shown, by considering the method over several steps, that the satisfaction of this condition leads to a reducibility in the method. Linking the symplectic criterion here to that for Runge-Kutta methods, we demonstrate that a general linear method is symplectic only if it can be reduced to a method with a single input value.
Original languageEnglish
Pages (from-to)77-84
Number of pages8
JournalNumerical Algorithms
Issue number1
Publication statusPublished - 2009


  • Reducibility
  • General linear methods
  • Symplectic


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