Symmetric multistep methods over long times

Authors:
Ernst Hairer;Christian Lubich
Affiliations:
Univ. de Genève, Dept. de Mathématiques, Switzerland;Univ. Tübingen, Mathematisches Institut, Germany
Venue:
Numerische Mathematik
Year:
2004

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Abstract

For computations of planetary motions with special linear multistep methods an excellent long-time behaviour is reported in the literature, without a theoretical explanation. Neither the total energy nor the angular momentum exhibit secular error terms. In this paper we completely explain this behaviour by studying the modified equation of these methods and by analyzing the remarkably stable propagation of parasitic solution components.