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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Numerical integrators based on modified differential equations


Authors: Philippe Chartier, Ernst Hairer and Gilles Vilmart
Journal: Math. Comp. 76 (2007), 1941-1953
MSC (2000): Primary 65L06, 65P10, 70E15
Published electronically: May 9, 2007
MathSciNet review: 2336275
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Abstract | References | Similar Articles | Additional Information

Abstract: Inspired by the theory of modified equations (backward error analysis), a new approach to high-order, structure-preserving numerical integrators for ordinary differential equations is developed. This approach is illustrated with the implicit midpoint rule applied to the full dynamics of the free rigid body. Special attention is paid to methods represented as B-series, for which explicit formulae for the modified differential equation are given. A new composition law on B-series, called substitution law, is presented.


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Additional Information

Philippe Chartier
Affiliation: INRIA Rennes, Campus Beaulieu, F-35042 Rennes, Cedex, France
Email: Philippe.Chartier@irisa.fr

Ernst Hairer
Affiliation: Section de Mathématiques, Université de Genève, CH-1211 Genève 4, Switzerland
Email: Ernst.Hairer@math.unige.ch

Gilles Vilmart
Affiliation: ENS Cachan Bretagne, Campus Ker-Lann, av. Robert Schumann, F-35170 Bruz, France
Email: Gilles.Vilmart@irisa.fr

DOI: http://dx.doi.org/10.1090/S0025-5718-07-01967-9
PII: S 0025-5718(07)01967-9
Keywords: Geometric numerical integration, modified differential equation, backward error analysis, modifying integrator, rigid body integrator, B-series, substitution law.
Received by editor(s): December 5, 2005
Received by editor(s) in revised form: August 1, 2006
Published electronically: May 9, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.