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unige:12123 
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Symmetric multistep methods over long times |
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| Published in | Numerische Mathematik. 2004, vol. 97, no. 4, p. 699-723 | |
| 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. | |
| Keywords | 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 | |
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Article (Author postprint) (1.7 MB) - Free access Other version: http://www.springerlink.com/content/k97kpj64d5l06uq7/ |
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| 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 https://archive-ouverte.unige.ch/unige:12123 |
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