Global Gronwall Estimates for Integral Curves on Riemannian Manifolds - Kunzinger, Michael; Schichl, Hermann; Steinbauer, Roland; Vickers, James A. (Revista Matemática Complutense, 2006)
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.