Optimization of Lie group methods for differential equations

Authors:
S. Blanes;F. Casas
Affiliations:
Departament de Matemàtiques, Universitat Jaume I, 12071 Castellón, Spain;Departament de Matemàtiques, Universitat Jaume I, 12071 Castellón, Spain
Venue:
Future Generation Computer Systems - Special issue: Geometric numerical algorithms
Year:
2003

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Abstract

In this paper we present a technique for reducing to a minimum the number of commutators required in the practical implementation of Lie group methods for integrating numerically matrix differential equations. This technique is subsequently applied to the linear and nonlinear case for constructing new geometric integrators, optimal with respect to the number of commutators.