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Suppression of the Wrapping Effect by Taylor Model-based Verified Integrators: The Single Step

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. In this paper we show how the former question can be treated within the framework of Taylor model methods, in which the dependence on initial conditions is expressed by a high-order multivariate polynomial and a remainder bound. Numerous examples of the performance of the method and comparisons to other approaches are given.

K. Makino, M. Berz, International Journal of Pure and Applied Mathematics 36(2) (2006) 175-197

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