Tech Report CS-01-05

A Constraint Satisfaction Approach for Enclosing Solutions to Parametric Ordinary Differential Equations

Micha Janssen, Pascal Van Hentenryck, and Yves Deville

July 2001

Abstract:

This paper 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 paper 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. 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 for complex problems.