Modified differential equations

Free access article

Issue		ESAIM: Proc. Volume 21, 2007 Journées d'analyse fonctionnelle et numérique en l'honneur de Michel Crouzeix


Page(s)		16 - 20
DOI		http://dx.doi.org/10.1051/proc:072102
Published online		04 December 2007

ESAIM: Proc., 2007, Vol. 21, pp. 16-20
DOI: 10.1051/proc:072102

Modified differential equations

Philippe Chartier¹, Ernst Hairer² and Gilles Vilmart^{1, 2}

¹ INRIA Rennes, Campus de Beaulieu, 35042 Rennes-Cedex, France
² Section de Mathématiques, Université de Genève, 2-4 rue du Lièvre, CH-1211 Genève 4, Switzerland

(... / Published online: 4 December 2007)

Abstract
Motivated by the theory of modified differential equations (backward error analysis) an approach for the construction of high order numerical integrators that preserve geometric properties of the exact flow is developed. This summarises a talk presented in honour of Michel Crouzeix.

Résumé
Motivé par la théorie des équations modifiées (analyse rétrograde de l'erreur), une approche pour la construction de méthodes numériques d'ordre élevé préservant des propriétés géométriques du flot exact est développée. Ceci résume une présentation donnée en honneur de Michel Crouzeix.

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