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On the order of iterated defect correction. An algebraic proof

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Published in Numerische Mathematik. 1978, vol. 29, no. 4, p. 409-424
Abstract In a recent article [2] Frank and Ueberhuber 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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Deposited on : 2010-11-19

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