Constraint Satisfaction in Ordinary Differential Equations
Micha Janssen
Broschiertes Buch

Constraint Satisfaction in Ordinary Differential Equations

Enclosing the Solution of the Initial Value Problem

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This work considers initial value problems (IVPs) 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 encl...