Preserving first integrals and volume forms of additively split systems

Philippe Chartier 1, 2 Murua Ander 3
1 IPSO - Invariant Preserving SOlvers
IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique
Abstract : This work is concerned with the preservation of invariants and of volume-forms by numerical methods which can be expanded into B-series. The situation we consider here is that of a split vector field where each sub-field either has the common invariant I or is divergence free. We derive algebraic conditions on the coefficients of the B-series for it either to preserve I or to preserve the volume for generic vector fields and interpret them for additive Runge-Kutta methods. Comparing the two sets of conditions then enables us to state some non-existence results. For a more restrictive class of problems, where the system is partitionned into several components, we nevertheless obtain simplified conditions and show that they can be solved.
Type de document :
[Research Report] RR-6016, INRIA. 2006, pp.27
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Contributeur : Rapport de Recherche Inria <>
Soumis le : lundi 13 novembre 2006 - 17:56:53
Dernière modification le : jeudi 15 novembre 2018 - 11:57:05
Document(s) archivé(s) le : lundi 27 juin 2011 - 15:32:37



  • HAL Id : inria-00113486, version 2


Philippe Chartier, Murua Ander. Preserving first integrals and volume forms of additively split systems. [Research Report] RR-6016, INRIA. 2006, pp.27. 〈inria-00113486v2〉



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