A Constraint Satisfaction Approach to Parametric Differential Equations

Abstract

Parametric ordinary differential equations arise in many areas of science and engineering. Since some of the data is uncertain and given by intervals, traditional numerical methods do not apply. Interval methods provide a way to approach these problems but they often suffer from a loss in precision and high computation costs. This paper presents a constraint satisfaction approach that enhances interval methods with a pruning step based on a global relaxation of the problem. Theoretical and experimental evaluations show that the approach produces significant improvements in accurracy and/or efficiency over the best interval methods. 1 Introduction Ordinary differential equations arise naturally in many applications in science and engineering, including chemistry, physics, molecular biology, and mechanics to name only a few. An ordinary differential equation (ODE) O is a system of the form u1 0 (t) = f1 (t; u1 (t); : : : ; un (t)) : : : un 0 (t) = fn (t; u1 (t); : : ...