Qualitative simulation and related approaches for the analysis of dynamic systems
The Knowledge Engineering Review
Validated solutions of initial value problems for parametric ODEs
Applied Numerical Mathematics
From model-checking to temporal logic constraint solving
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
Localization of an underwater robot using interval constraint propagation
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
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This paper considers initial value problems 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 work 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. The relaxation uses Hermite interpolation polynomials and enclosures of their error terms to approximate the ODE. Our work also shows how to find an evaluation time for the relaxation that minimizes its local error. 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 when the ODE contains many operations.