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

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. The Taylor model approach is very well suited to overcome the problems of short term flow representation. In this paper we discuss a method based on preconditioning that stabilizes the long-term evolution of the flow. Examples of the performance of the method and comparisons to other approaches are given.

K. Makino, M. Berz, International Journal of Differential Equations and Applications 10(4) (2005) 353-384. This paper won the 3rd Moore Prize for Applications of Interval Analysis in 2008.

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