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Symmetric multistep methods over long times

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Summary.

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.

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Authors and Affiliations

  1. Dept. de Mathématiques, Univ. de Genève, 1211, Genève 24, Switzerland

    Ernst Hairer

  2. Mathematisches Institut, Univ. Tübingen, 72076, Tübingen, Germany

    Christian Lubich

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  1. Ernst Hairer
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  2. Christian Lubich
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Correspondence to Ernst Hairer.

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Mathematics Subject Classification (1991): 65L06, 65P10

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Hairer, E., Lubich, C. Symmetric multistep methods over long times. Numer. Math. 97, 699–723 (2004). https://doi.org/10.1007/s00211-004-0520-2

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  • DOI: https://doi.org/10.1007/s00211-004-0520-2

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