Global Gronwall Estimates for Integral Curves on Riemannian Manifolds
Differential Geometry
2007-05-23 v3 Classical Analysis and ODEs
Abstract
We prove Gronwall-type estimates for the distance of integral curves of smooth vector fields on a Riemannian manifold. Such estimates are of central importance for all methods of solving ODEs in a verified way, i.e., with full control of roundoff errors. Our results may therefore be seen as a prerequisite for the generalization of such methods to the setting of Riemannian manifolds.
Keywords
Cite
@article{arxiv.math/0412045,
title = {Global Gronwall Estimates for Integral Curves on Riemannian Manifolds},
author = {Michael Kunzinger and Hermann Schichl and Roland Steinbauer and James A. Vickers},
journal= {arXiv preprint arXiv:math/0412045},
year = {2007}
}
Comments
4 pages, 1 figure, correction of some misprints