A New Perspective on the Wrapping Effect in Interval Methods for Initial Value Problems for Ordinary Differential Equations

Abstract

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.