Martin Berz and Kyoko Makino
Department of Physics and Astronomy
Michigan State University
East Lansing, MI 48824, USA
email: berz@msu.edu
Abstract:
The performance of various Taylor model (TM)-based methods for the validated integration of ODEs is studied for a representative class of 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.