Global Gronwall estimates for integral curves on Riemannian manifolds
Global Gronwall estimates for integral curves on Riemannian manifolds
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.
riemannian geometry, ordinary differential equations, gronwall estimate
133-137
Kunzinger, Michael
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Schichl, Hermann
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Steinbauer, Roland
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Vickers, James A.
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Kunzinger, Michael
5ee9f681-a923-4fb5-b1c8-9454237dd721
Schichl, Hermann
1929db20-e8bb-434d-92b0-28fa52b7e6a6
Steinbauer, Roland
053836b9-b9d0-4a1d-93b1-06500bc87b17
Vickers, James A.
719cd73f-c462-417d-a341-0b042db88634
Kunzinger, Michael, Schichl, Hermann, Steinbauer, Roland and Vickers, James A.
(2005)
Global Gronwall estimates for integral curves on Riemannian manifolds.
Revista Matemática Complutense, 19 (1), .
(Submitted)
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.
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Submitted date: 13 June 2005
Keywords:
riemannian geometry, ordinary differential equations, gronwall estimate
Identifiers
Local EPrints ID: 39012
URI: http://eprints.soton.ac.uk/id/eprint/39012
ISSN: 1139-1138
PURE UUID: d8a1d40a-6996-4ed2-8839-635aa2e3e7d6
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Date deposited: 19 Jun 2006
Last modified: 12 Dec 2021 02:33
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Contributors
Author:
Michael Kunzinger
Author:
Hermann Schichl
Author:
Roland Steinbauer
Author:
James A. Vickers
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