Invariant connections, Lie algebra actions, and foundations of numerical integration on manifolds
Differential Geometry
2020-02-24 v1 Numerical Analysis
Rings and Algebras
Abstract
Motivated by numerical integration on manifolds, we relate the algebraic properties of invariant connections to their geometric properties. Using this perspective, we generalize some classical results of Cartan and Nomizu to invariant connections on algebroids. This has fundamental consequences for the theory of numerical integrators, giving a characterization of the spaces on which Butcher and Lie-Butcher series methods, which generalize Runge-Kutta methods, may be applied.
Keywords
Cite
@article{arxiv.1903.10056,
title = {Invariant connections, Lie algebra actions, and foundations of numerical integration on manifolds},
author = {Hans Z. Munthe-Kaas and Ari Stern and Olivier Verdier},
journal= {arXiv preprint arXiv:1903.10056},
year = {2020}
}
Comments
18 pages