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

du Abstract. The problem of reducing the wrapping effect in interval methods for initial value problems for ordinary differential equations has usually been studied from a geometric point of view. We develop a new perspective on this problem by linking the wrapping effect to the stability of the interval method. Thus, reducing the wrapping effect is related to finding a more stable scheme for advancing the so­ lution. This allows us to exploit eigenvalue techniques and to avoid the complicated geometric arguments used previously. We study the stability of several anti-wrapping schemes, including Lohner's QR-factorization method, which we show can be viewed as a simultaneous iteration for computing the eigenvalues of an associated matrix. Using this connection, we explain how Lohner's method improves the stability of an interval method and show that, for a large class of problems, its global error is not much bigger than that of the corresponding point method.

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