The non-existence of symplectic multi-derivative Runge-Kutta methods
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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 classification65L06 70H15
Key wordsMulti-derivative Runge-Kutta methods symplectic methods irreducible methods
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