| Type de publication : |
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Rapport de recherche |
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| Domaine : |
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Mathématiques/Analyse numérique
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| Titre : |
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Preserving first integrals and volume forms of additively split systems |
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| Auteur(s) : |
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Philippe Chartier ( ) 1, 2, Murua Ander 3 |
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| Projet(s) / laboratoire(s) : |
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| Résumé : |
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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. |
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| Classification ACM : |
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G.: Mathematics of Computing/G.1: NUMERICAL ANALYSIS |
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| Langue du document : |
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Anglais |
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| Type de rapport : |
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Rapport de recherche |
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| Nombre de pages : |
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27 |
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| Date de publication : |
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2006 |
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| Mots-clés : |
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polynomial invariants – volume-form – split systems – B-series – S-series |
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| Date de rédaction : |
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2006 |
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| Référence interne : |
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RR-6016 |
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