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Suppression of the Wrapping Effect by Taylor Model- based Validated Integrators


Abstract

The validated 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 methods how this can be achieved within the framework of Taylor model methods, in which the dependence on intial conditions is expressed by a high-order multivariate polynomial and a remainder bound. Numerous examples of the performance of the methods and comparisons to other approaches are given.


K. Makino, M. Berz, MSU HEP Report 40910 (2003)


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