IJPAM: Volume 36, No. 2 (2007)

SUPPRESSION OF THE WRAPPING EFFECT BY
TAYLOR MODEL - BASED VERIFIED INTEGRATORS:
THE SINGLE STEP

Kyoko Makino$^1$, Martin Berz$^2$
$^{1}$Department of Physics
University of Illinois at Urbana-Champaign
1110 W. Green Street, Urbana, IL 61801-3080, USA
$^{2}$Department of Physics and Astronomy
Michigan State University
East Lansing, MI 48824, USA
e-mail: berz@msu.edu


Abstract.The verified 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. In this paper we show how the former question can be treated within the framework of Taylor model methods, in which the dependence on initial conditions is expressed by a high-order multivariate polynomial and a remainder bound. Numerous examples of the performance of the method and comparisons to other approaches are given.

Received: July 2, 2006

AMS Subject Classification: 65L05, 65G20, 34-04, 41A58

Key Words and Phrases: differential equations, ODE, initial value problem, IVP, Taylor integration, verification, rigorous computation, wrapping effect, preconditioning, QR method, Taylor model, interval method

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 36
Issue: 2