On the Global Error of Discretization Methods for Highly-Oscillatory Ordinary Differential Equations (2000)
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BibTeX
@MISC{Iserles00onthe,
author = {Arieh Iserles},
title = {On the Global Error of Discretization Methods for Highly-Oscillatory Ordinary Differential Equations},
year = {2000}
}
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Abstract
Commencing from a global-error formula, originally due to Henrici, we investigate the accumulation of global error in the numerical solution of linear highly-oscillating systems of the form y 00 + g(t)y = 0, where g(t) t!1 \Gamma! 1. Using WKB analysis we derive an explicit form of the global-error envelope for Runge-Kutta and Magnus methods. Our results are closely matched by numerical experiments. Motivated by the superior performance of Lie-group methods, we present a modification of the Magnus expansion which displays even better long-term behaviour in the presence of oscillations.
