Performance of taylor model methods for validated integration of ODEs

Authors:
Martin Berz;Kyoko Makino
Affiliations:
Department of Physics and Astronomy, Michigan State University, East Lansing, MI;Department of Physics and Astronomy, Michigan State University, East Lansing, MI
Venue:
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
Year:
2004

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Abstract

The performance of various Taylor model (TM)-based methods for the validated integration of ODEs is studied for some representative computational problems. For nonlinear problems, the advantage of the method lies in the ability to retain dependencies of final conditions on initial conditions to high order, leading to the ability to treat large boxes of initial conditions for extended periods of time. For linear problems, the asymptotic behavior of the error of the methods is seen to be similar to that of non-validated integrators.