Convergence of Lie group integrators

TL;DR

This paper establishes a connection between local and global error estimates for Lie group integrators on Riemannian homogeneous spaces, demonstrating that Lie-Butcher theory can be used to derive global error bounds for these schemes.

Contribution

It is the first to show how Lie-Butcher theory provides global error estimates for Lie group integrators on Riemannian homogeneous spaces.

Findings

Global error estimates can be derived from local bounds.

Lie-Butcher theory applies to Lie group integrators.

First proof connecting Lie-Butcher theory with global error analysis.

Abstract

We relate two notions of local error for integration schemes on Riemannian homogeneous spaces, and show how to derive global error estimates from such local bounds. In doing so, we prove for the first time that the Lie-Butcher theory of Lie group integrators leads to global error estimates.