Enclosing Temporal Evolution of Dynamical Systems Using Numerical Methods

International audienceNumerical 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