English

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