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v1 (2006-11-13)

v2 (2006-11-13)

Preserving first integrals and volume forms of additively split systems

Philippe Chartier 1, 2, Murua Ander 3

(2006)

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.

1:	IPSO (INRIA - IRMAR)
	CNRS : UMR6074 – INRIA – Université de Rennes 1
2:	Institut de Recherche Mathématique de Rennes (IRMAR)
	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
3:	Computer Science Department [San Sebastian]
	Universidad del País Vasco

Domain

:

Mathematics/Numerical Analysis

Keywords: polynomial invariants – volume-form – split systems – B-series – S-series

inria-00113486, version 2

http://hal.inria.fr/inria-00113486

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From: Rapport De Recherche Inria <>

Submitted on: Monday, 13 November 2006 17:56:53

Updated on: Thursday, 25 March 2010 16:07:02