Consistency Techniques in Ordinary Differential Equations

Authors:
Yves Deville;Micha Janssen;Pascal Van Hentenryck
Affiliations:
-;-;-
Venue:
CP '98 Proceedings of the 4th International Conference on Principles and Practice of Constraint Programming
Year:
1998

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Abstract

This paper studies the application of interval analysis and consistency techniques to ordinary differential equations. It presents a unifying framework to extend traditional numerical techniques to intervals. In particular, it shows how to extend explicit methods to intervals. The paper also took a fresh look at the traditional problems encountered by interval techniques and studied how consistency techniques may help. It proposes to generalize interval techniques into a two-step process: a forward process that computes an enclosure and a backward process that reduces this enclosure. In addition, the paper studies how consistency techniques may help in improving the forward process and the wrapping effect.