Shrink wrapping for Taylor models revisited

Abstract

Taylor models have been used successfully to calculate verified inclusions of the solutions of initial value problems for ordinary differential equations. In this context, Makino and Berz introduced an accompanying method called shrink wrapping. This method aims to reduce the wrapping effect which occurs during repeated forward integration of Taylor models. We review shrink wrapping as proposed by Makino and Berz, state examples that point to a flaw in their theorem and concept of proof, and present a new, corrected version of shrink wrapping.