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Title

Symmetric multistep methods over long times

Authors
Lubich, Christian
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 methodHamiltonian systemN-body systemEnergy conservationConservation of angular momentumSymplecticityInvariant toriLinear error growthBackward error analysisModified differential equationModulated Fourier expansion
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HAIRER, Ernst, LUBICH, Christian. Symmetric multistep methods over long times. In: Numerische Mathematik, 2004, vol. 97, n° 4, p. 699-723. https://archive-ouverte.unige.ch/unige:12123

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Deposited on : 2010-10-18

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