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Numerische Mathematik

, Volume 97, Issue 4, pp 699–723 | Cite as

Symmetric multistep methods over long times

  • Ernst HairerEmail author
  • Christian Lubich
Article

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.

Keywords

Total Energy Angular Momentum Error Term Theoretical Explanation Stable Propagation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Dept. de MathématiquesUniv. de GenèveGenève 24Switzerland
  2. 2.Mathematisches InstitutUniv. TübingenTübingenGermany

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