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Suppression of the Wrapping Effect by Taylor Model-based Verified Integrators: Long-term Stabilization by Shrink Wrapping

Abstract

The verified integration of ranges of initial conditons through ODEs faces two major challenges, namely the precise representation of the flow over the short term, and the avoidance of unfavorable buildup of errors in the long term. We discuss the method of shrink wrapping for meeting the second of these challenges within the framework of Taylor model methods. Illustrative examples of the performance of the method and comparisons to other approaches are given.

M. Berz, K. Makino, International Journal of Differential Equations and Applications 10(4) (2005) 385-403

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