Abstract
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.
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References
Hairer, E., Lubich, C., Wanner, G.: Geometric Numerical Integration. Springer, Berlin (2002)
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Butcher, J.C., Hewitt, L.L. The existence of symplectic general linear methods. Numer Algor 51, 77–84 (2009). https://doi.org/10.1007/s11075-008-9250-3
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DOI: https://doi.org/10.1007/s11075-008-9250-3