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.
@article{urn:eudml:doc:40879,
title = {Global Gronwall estimates for integral curves on Riemannian manifolds.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {19},
year = {2006},
pages = {133-137},
zbl = {1095.53029},
mrnumber = {MR2219824},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40879}
}
Kunzinger, Michael; Schichl, Hermann; Steinbauer, Roland; Vickers, James A. Global Gronwall estimates for integral curves on Riemannian manifolds.. Revista Matemática de la Universidad Complutense de Madrid, Tome 19 (2006) pp. 133-137. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40879/