2001 | OriginalPaper | Buchkapitel
A New Perspective on the Wrapping Effect in Interval Methods for Initial Value Problems for Ordinary Differential Equations
verfasst von : Nedialko S. Nedialkov, Kenneth R. Jackson
Erschienen in: Perspectives on Enclosure Methods
Verlag: Springer Vienna
Enthalten in: Professional Book Archive
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The problem of reducing the wrapping effeet in interval methods for initial value problems for ordinary differential equations has usually been studied from a geometrie point of view. We develop a new perspeetive on this problem by linking the wrapping effeet to the stability of the interval method. Thus, redueing the wrapping effect is related to finding a more stable seheme for advaneing the solution. This allows us to exploit eigenvalue teehniques and to avoid the eomplieated geometrie arguments used previously.