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Enclosing Temporal Evolution of Dynamical Systems Using Numerical Methods

Olivier Bouissou 1, * Alexandre Chapoutot 2 Adel Djoudi 2
* Corresponding author
1 LMeASI - Laboratoire Modélisation et Analyse de Systèmes en Interaction
LIST - Laboratoire d'Intégration des Systèmes et des Technologies : DRT/LIST
Abstract : Numerical methods are necessary to understand the behav- iors of complex hybrid systems used to design control-command systems. Especially, numerical integration methods are heavily used in simulation to compute approximations of the solution of differential equations, in- cluding non-linear and stiff solutions. Nevertheless, these methods only produce approximate results and they should not be used in formal ver- ification methods as is. We propose a systematic way to make explicit Runge-Kutta integration method safe with respect to the mathemati- cal solution. As side effect, we can hence compare different integration schemes in order to pick the right one in different situations.
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Submitted on : Thursday, May 2, 2013 - 10:40:52 AM
Last modification on : Friday, June 25, 2021 - 9:48:02 AM

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Olivier Bouissou, Alexandre Chapoutot, Adel Djoudi. Enclosing Temporal Evolution of Dynamical Systems Using Numerical Methods. 5th NASA Formal Methods Symposium, 7871, Springer Verlag, pp.108, 2013, LNCS, ⟨10.1007/978-3-642-38088-4_8⟩. ⟨hal-00819730⟩



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