The non-existence of symplectic multi-derivative Runge-Kutta methods |
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| Authors: | E Hairer A Murua J M Sanz-Serna |
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| Institution: | (1) Dept. de mathématiques, Université de Genève, Case postale 240, CH.1211 Genève 24, Switzerland;(2) Informatika Fakultatea, Euskal Herriko Unibertsitatea, 649 Postakutxa, 20080 San Sebastian, Spain;(3) Departamento de Matemática Aplicada y Computación, Facultad de Ciencias, Universidad de Valladolid, Valladolid, Spain |
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| 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 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.This research has been supported by project PB89-0351 (Dirección General de Investigación Científica y Técnica) and by project No. 20-32354.91 of Swiss National Science Foundation. |
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| Keywords: | 65L06 70H15 |
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