On the order of iterated defect correction |
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Authors: | E Hairer |
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Institution: | (1) Institut für Mathematik der Universität Innsbruck, Innrain 52, A-6020 Innsbruck, Austria |
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Abstract: | Summary In a recent article 2] Frank and Überhuber define and motivate the method of iterated defect correction for Runge-Kutta methods. They prove a theorem on the order of that method using the theory of asymptotic expansions.In this paper we give similar results using the theory of Butcher series (see 4]). Our proofs are purely algebraic. We don't restrict our considerations to Runge-Kutta methods, but we admit arbitrary linear one-step methods. At the same time we consider more general defect functions as in 2]. |
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Keywords: | AMS (MOS): 65LO5 CR: 5 17 |
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