---
title: "A Constraint Satisfaction Approach to Parametric Differential Equations"
authors:
  - "Micha Janssen"
  - "Pascal Van Hentenryck"
  - "Yves Deville"
doi: ""
url: "https://ijcai.org/proceedings/2001/42"
pdf: "https://ijcai.org/proceedings/2001/0042.pdf"
venue: "Proceedings of the Seventeenth International Joint Conference on Artificial Intelligence"
year: 2001
pages: "297-301"
track: ""
keywords:
---

# A Constraint Satisfaction Approach to Parametric Differential Equations

Micha Janssen, Pascal Van Hentenryck, Yves Deville

*Proceedings of the Seventeenth International Joint Conference on Artificial Intelligence*, pages 297-301.

## Abstract

Initial value problems for 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 accuracy and/or efficiency over the best interval methods.