Backward error analysis for multistep methods |
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Authors: | Ernst Hairer |
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Institution: | (1) Dept. de Mathématiques, Université de Genève, CH-1211 Genève 24, Switzerland; e-mail: Ernst.Hairer@math.unige.ch; http://www.unige.ch/math/folks/hairer/ , CH |
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Abstract: | Summary. In recent years, much insight into the numerical solution of ordinary differential equations by one-step methods has been
obtained with a backward error analysis. It allows one to explain interesting phenomena such as the almost conservation of
energy, the linear error growth in Hamiltonian systems, and the existence of periodic solutions and invariant tori. In the
present article, the formal backward error analysis as well as rigorous, exponentially small error estimates are extended
to multistep methods. A further extension to partitioned multistep methods is outlined, and numerical illustrations of the
theoretical results are presented.
Received January 20, 1998 / Revised version received November 20, 1998 / Published online September 24, 1999 |
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Keywords: | Mathematics Subject Classification (1991):65L06 |
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