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Asymptotic expansions of the global error of fixed-stepsize methods

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Lubich, Christian
Published in Numerische Mathematik. 1984, vol. 45, no. 3, p. 345-360
Abstract In his fundamental paper on general fixed-stepsize methods, Skeel [6] studied convergence properties, but left the existence of asymptotic expansions as an open problem. In this paper we give a complete answer to this question. For the special cases of one-step and linear multistep methods our proof is shorter than the published ones. Asymptotic expansions are the theoretical base for extrapolation methods.
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HAIRER, Ernst, LUBICH, Christian. Asymptotic expansions of the global error of fixed-stepsize methods. In: Numerische Mathematik, 1984, vol. 45, n° 3, p. 345-360. https://archive-ouverte.unige.ch/unige:12464

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Deposited on : 2010-11-15

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