Differential equations and dynamical systems
Differential equations and dynamical systems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Consistency Techniques in Ordinary Differential Equations
CP '98 Proceedings of the 4th International Conference on Principles and Practice of Constraint Programming
Multistep Filtering Operators for Ordinary Differential Equations
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
Computing rigorous bounds on the solution of an initial value problem for an ordinary differential equation
Numerica: a modeling language for global optimization
IJCAI'97 Proceedings of the Fifteenth international joint conference on Artifical intelligence - Volume 2
A constraint satisfaction approach to parametric differential equations
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Constraint Reasoning for Differential Models
Proceedings of the 2005 conference on Constraint Reasoning for Differential Models
Constraint reasoning in deep biomedical models
Artificial Intelligence in Medicine
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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.