Full paper in PDF:
$%M. Kunzinger, H. Schichl, R. Steinbauer, and J. A. Vickers, Global Gronwall estimates for integral
curves on Riemannian manifolds, Rev. Mat. Complut. 19 (2006), no. 1, 133–137.
%$
Fakultät für Mathematik
Universität Wien Nordbergstrasse 15 1090 Wien — Austria
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School of Mathematics University of Southampton Highfield, Southampton SO 17 1BJ — UK |
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.
Key words: Riemannian geometry, ordinary differential equations, Gronwall estimate.
2000 Mathematics Subject Classification: 53B21, 53C22, 34A26.