Abstract
Numerical methods are necessary to understand the behaviors 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, including non-linear and stiff solutions. Nevertheless, these methods only produce approximate results and they should not be used in formal verification methods as is. We propose a systematic way to make explicit Runge-Kutta integration method safe with respect to the mathematical solution. As side effect, we can hence compare different integration schemes in order to pick the right one in different situations.
This work was partially supported by the ANR project CAFEIN.
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Bouissou, O., Chapoutot, A., Djoudi, A. (2013). Enclosing Temporal Evolution of Dynamical Systems Using Numerical Methods. In: Brat, G., Rungta, N., Venet, A. (eds) NASA Formal Methods. NFM 2013. Lecture Notes in Computer Science, vol 7871. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38088-4_8
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DOI: https://doi.org/10.1007/978-3-642-38088-4_8
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