Scientific article
Open access

Symmetric multistep methods over long times

Published inNumerische Mathematik, vol. 97, no. 4, p. 699-723
Publication date2004

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.

  • Linear multistep method
  • Hamiltonian system
  • N-body system
  • Energy conservation
  • Conservation of angular momentum
  • Symplecticity
  • Invariant tori
  • Linear error growth
  • Backward error analysis
  • Modified differential equation
  • Modulated Fourier expansion
Citation (ISO format)
HAIRER, Ernst, LUBICH, Christian. Symmetric multistep methods over long times. In: Numerische Mathematik, 2004, vol. 97, n° 4, p. 699–723. doi: 10.1007/s00211-004-0520-2
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Article (Accepted version)
ISSN of the journal0029-599X

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