Convergence of Lie group integrators
arXiv:1807.118295 citationsh-index: 12
AI Analysis
Provides a theoretical foundation for error analysis of Lie group integrators, benefiting researchers in numerical analysis and geometric integration.
The paper establishes a connection between local and global error estimates for integration schemes on Riemannian homogeneous spaces, proving for the first time that Lie-Butcher theory yields global error bounds.
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.