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

Murua, Ander
Sanz-Serna, Jesus Maria
Published in BIT Numerical Mathematics. 1994, vol. 34, no. 1, p. 80-87
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 with q<=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.
Keywords Multi-derivative Runge-Kutta methodsSymplectic methodsIrreducible methods
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HAIRER, Ernst, MURUA, Ander, SANZ-SERNA, Jesus Maria. The non-existence of symplectic multi-derivative Runge-Kutta methods. In: BIT Numerical Mathematics, 1994, vol. 34, n° 1, p. 80-87. https://archive-ouverte.unige.ch/unige:12479

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