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Equivariant Series
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We show that if a numerical integrator is both equivariant and local on a homogeneous space, then it can be developed in an equivariant series, which generalises the standard B-Series. In the affine case, we have an explicit description of equivariant series in terms of elementary differentials associated to aromatic trees, which are generalisation of trees. We also define a new class of integrators, that extends Runge-Kutta methods, and which we conjecture to be dense in the whole possible range of local and affine equivariant integrators.

National Category
Computational Mathematics
URN: urn:nbn:se:umu:diva-80259OAI: diva2:647934
Available from: 2013-09-12 Created: 2013-09-12 Last updated: 2014-04-22

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Verdier, Olivier
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Department of Mathematics and Mathematical Statistics
Computational Mathematics

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