On the Global Error of Discretization Methods for Highly-oscillatory Ordinary Diierential Equations
نویسنده
چکیده
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 ?! 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 modiication of the Magnus expansion which displays even better long-term behaviour in the presence of oscillations.
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