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Lie-group methods

Published online by Cambridge University Press:  21 March 2001

Arieh Iserles ,
Hans Z. Munthe-Kaas ,
Syvert P. Nørsett  and
Antonella Zanna
Arieh Iserles
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England. E-mail: a.iserles@damtp.cam.ac.uk
Hans Z. Munthe-Kaas
Affiliation:
Department of Computer Science, University of Bergen, Norway. E-mail: hans@ii.uib.no
Syvert P. Nørsett
Affiliation:
Institute of Mathematics, Norwegian University of Science and Technology, Trondheim, Norway. E-mail: norsett@math.ntnu.no
Antonella Zanna
Affiliation:
Department of Computer Science, University of Bergen, Norway. E-mail: anto@ii.uib.no
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Abstract

Many differential equations of practical interest evolve on Lie groups or on manifolds acted upon by Lie groups. The retention of Lie-group structure under discretization is often vital in the recovery of qualitatively correct geometry and dynamics and in the minimization of numerical error. Having introduced requisite elements of differential geometry, this paper surveys the novel theory of numerical integrators that respect Lie-group structure, highlighting theory, algorithmic issues and a number of applications.

Type
Research Article
Information
Acta Numerica , Volume 9 , January 2000 , pp. 215 - 365
Copyright
© Cambridge University Press 2000

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