Pseudo-symplectic Runge-Kutta methods |
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Authors: | A Aubry P Chartier |
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Institution: | (1) IRISA, Campus de Beaulieu, 35042 Rennes Cedex, France;(2) INRIA, Campus de Beaulieu, 35042 Rennes Cedex, France |
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Abstract: | Apart from specific methods amenable to specific problems, symplectic Runge-Kutta methods are necessarily implicit. The aim
of this paper is to construct explicit Runge-Kutta methods which mimic symplectic ones as far as the linear growth of the
global error is concerned. Such method of orderp have to bepseudo-symplectic of pseudosymplecticness order2p, i.e. to preserve the symplectic form to within ⊗(h
2p
)-terms. Pseudo-symplecticness conditions are then derived and the effective construction of methods discussed. Finally, the
performances of the new methods are illustrated on several test problems. |
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Keywords: | 65L05 |
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