(English)Manuscript (preprint) (Other academic)
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.
IdentifiersURN: urn:nbn:se:umu:diva-80259OAI: oai:DiVA.org:umu-80259DiVA: diva2:647934