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| HAL: inria-00113486, version 2 |
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| Available versions | v2 (2006-11-13) |
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| Preserving first integrals and volume forms of additively split systems |
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| Philippe Chartier 1, 2Murua Ander 3 |
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| (2006) |
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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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| 1: | IPSO (INRIA - IRMAR) |
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CNRS : UMR6074 – INRIA – Université de Rennes 1 |
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| 2: | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| 3: | Computer Science Department [San Sebastian] |
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Universidad del País Vasco |
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| Domain | : | Mathematics/Numerical Analysis |
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| polynomial invariants – volume-form – split systems – B-series – S-series |
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| inria-00113486, version 2 | |
| http://hal.inria.fr/inria-00113486 | |
| oai:hal.inria.fr:inria-00113486 | |
| From: Rapport De Recherche Inria | |
| Submitted on: Monday, 13 November 2006 17:56:53 | |
| Updated on: Thursday, 25 March 2010 16:07:02 | |
