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Abstract: The Alekseev-Gröbner lemma is combined with the theory of modified equations to obtain an a priori estimate for the global error of numerical integrators. This estimate is correct up to a remainder term of order h^2p where h denotes the step size and p the order of the method. It is applied to a class of nonautonomous linear oscillatory equations, which includes the Airy equation, thereby improving prior work which only gave the h^p term. However, the result is not very surprising. Next, a... (Update)
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BibTeX entry: (Update)
@misc{ niesen-priori,
author = "Jitse Niesen",
title = "A Priori Estimates for the Global Error Committed by {R}unge-{K}utta Methods
for a Nonlinear Oscillator",
url = "citeseer.ist.psu.edu/niesen01priori.html" }
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