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