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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.
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https://hal.inria.fr/inria-00113486
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Submitted on : Monday, November 13, 2006 - 5:56:53 PM
Last modification on : Friday, May 20, 2022 - 9:04:52 AM
Long-term archiving on: : Monday, June 27, 2011 - 3:32:37 PM

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  • HAL Id : inria-00113486, version 2

Citation

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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