Constraint Satisfaction in Ordinary Differential Equations : Enclosing the Solution of the Initial Value Problem

ISBN-13: 9783639118728 / Angielski / Miękka / 2009 / 152 str.

Micha Janssen

Opis

This work considers initial value problems (IVPs) for ordinary differential equations (ODEs) where some of the data is uncertain and given by intervals as is the case in many areas of science and engineering. Interval methods provide a way to approach these problems but they raise fundamental challenges in obtaining high accuracy and low computation costs. This work introduces a constraint satisfaction approach to these problems which enhances traditional interval methods with a pruning step based on a global relaxation of the ODE. The relaxation uses Hermite interpolation polynomials and enclosures of their error terms to approximate the ODE. Our work also shows how to find an evaluation time for the relaxation that minimizes its local error. Theoretical and experimental results show that the approach produces significant improvements in accuracy over the best interval methods for the same computation costs. The results also indicate that the new algorithm should be significantly faster when the ODE contains many operations.

O autorze

Dr. Micha Janssen is a civil engineer in computer science and
holds a Ph.D. in applied science from the Université catholique
de Louvain (Belgium). He currently is a software engineer and a
project leader in Air Traffic Management.