Optimal pruning in parametric differential equations
(2001) Proceedings of 7th International Conference on Principles and Practice of Constraint Programming — Location: Paphos, Cyprus (26.November.2001)
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- Abstract
- Initial value problems for parametric ordinary differential equations (ODEs) arise in many areas of science and engineering. Since some of the data is uncertain, traditional numerical methods do not apply. This paper considers a constraint satisfaction approach that enhances traditional interval methods with a pruning component which uses a relaxation of the ODE and Hermite interpolation polynomials. It solves the main theoretical and practical open issue left in this approach: the choice of an optimal evaluation time for the relaxation. As a consequence, the constraint satisfaction approach is shown to provide a quadratic (asymptotical) improvement in accuracy over the best interval methods, while improving their running times. Experimental results confirm the theoretical results.
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Janssen, M., Van Hentenryck, P., & Deville, Y. (2001). Optimal pruning in parametric differential equations. In Walsh, T.; (ed.), Principles and Practice of Constraint Programming - CP 2002. 7thInternational Conference, CP 2001. Proceedings (Lecture Notes inComputer Science Vol.2239) (p. p. 539-553). Springer-verlag. https://hdl.handle.net/2078.5/225598