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Reports (Research Report) Year : 2006

Preserving first integrals and volume forms of additively split systems

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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Dates and versions

inria-00113486 , version 1 (13-11-2006)
inria-00113486 , version 2 (13-11-2006)

Identifiers

  • HAL Id : inria-00113486 , version 2

Cite

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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