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| HAL: inria-00070509, version 1 |
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| A substitution law for B-series vector fields |
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| Philippe Chartier 1, 2Ernst Hairer 3 |
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| (2005) |
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| In this paper, we derive a new composition law obtained by substituting a B-series into the vector field appearing in another B-series. We derive explicit formulas for the computation of this law and study its algebraic properties. We then focus on the specific case of Hamiltonian vector fields. It is shown that this new law allows a convenient derivation of the modified equation occurring in backward error analysis or in numerical methods based on generating functions. |
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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: | Section de mathématiques [Genève] |
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University of Geneva |
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| 4: | Ecole Normale Supérieure de Cachan (ENS Cachan) |
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École normale supérieure de Cachan - ENS Cachan |
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| Domain | : | Computer Science/Other |
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| ORDINARY DIFFERENTIAL EQUATIONS / B-SERIES / BACKWARD ERROR ANALYSIS / HAMILTONIAN / SYMPLECTIC / SYMMETRIC / GENERATING FUNCTION METHODS |
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| inria-00070509, version 1 | |
| http://hal.inria.fr/inria-00070509 | |
| oai:hal.inria.fr:inria-00070509 | |
| From: Rapport De Recherche Inria | |
| Submitted on: Friday, 19 May 2006 20:42:57 | |
| Updated on: Thursday, 25 March 2010 16:02:02 | |
