Global Gronwall estimates for integral curves on Riemannian manifolds.

Kunzinger, Michael, et al. "Global Gronwall estimates for integral curves on Riemannian manifolds.." Revista Matemática Complutense 19.1 (2006): 133-137. <http://eudml.org/doc/40879>.

@article{Kunzinger2006,
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.},
author = {Kunzinger, Michael, Schichl, Hermann, Steinbauer, Roland, Vickers, James A.},
journal = {Revista Matemática Complutense},
keywords = {Variedad riemanniana; Campos vectoriales; Geodésicas; Ecuaciones diferenciales ordinarias; Riemannian geometry; ordinary differential equations; Gronwall estimate; ODEs},
language = {eng},
number = {1},
pages = {133-137},
title = {Global Gronwall estimates for integral curves on Riemannian manifolds.},
url = {http://eudml.org/doc/40879},
volume = {19},
year = {2006},
}

TY - JOUR
AU - Kunzinger, Michael
AU - Schichl, Hermann
AU - Steinbauer, Roland
AU - Vickers, James A.
TI - Global Gronwall estimates for integral curves on Riemannian manifolds.
JO - Revista Matemática Complutense
PY - 2006
VL - 19
IS - 1
SP - 133
EP - 137
AB - 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.
LA - eng
KW - Variedad riemanniana; Campos vectoriales; Geodésicas; Ecuaciones diferenciales ordinarias; Riemannian geometry; ordinary differential equations; Gronwall estimate; ODEs
UR - http://eudml.org/doc/40879
ER -