$C^r$-Lohner algorithm

Details $C^r$-Lohner algorithm $C^r$-Lohner algorithm

2007-04-05

arxiv.org/abs/0704.0720v1

Mathematics

Numerical Analysis

for associated movie file, see http://www.ii.uj.edu.pl/~wilczak/papers/cnlohner/mpp.mov, 35 pages, 1 Figure

Scientific paper

We present a Lohner type algorithm for the computation of rigorous bounds for
solutions of ordinary differential equations and its derivatives with respect
to initial conditions up to arbitrary order. As an application we prove the
existence of multiple invariant tori around some elliptic periodic orbits for
the pendulum equation with periodic forcing and for Michelson system.

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