@misc{Auer_Ekaterina_A,
 author={Auer, Ekaterina and Kiel, Stefan and Rauh, Andreas},
 howpublished={online},
 publisher={Zielona Góra: Uniwersytet Zielonogórski},
 language={eng},
 abstract={In many applications, there is a need to choose mathematical models that depend on non-smooth functions. The task of simulation becomes especially difficult if such functions appear on the right-hand side of an initial value problem. Moreover, solution processes from usual numerics are sensitive to roundoff errors so that verified analysis might be more useful if a guarantee of correctness is required or if the system model is influenced by uncertainty.},
 abstract={In this paper, we provide a short overview of possibilities to formulate non-smooth problems and point out connections between the traditional non-smooth theory and interval analysis. Moreover, we summarize already existing verified methods for solving initial value problems with non-smooth (in fact, even not absolutely continuous) right-hand sides and propose a way of handling a certain practically relevant subclass of such systems.},
 abstract={We implement the approach for the solver VALENCIA-IVP by introducing into it a specialized template for enclosing the first-order derivatives of non-smooth functions. We demonstrate the applicability of our technique using a mechanical system model with friction and hysteresis. We conclude the paper by giving a perspective on future research directions in this area.},
 type={artykuł},
 title={A verified method for solving piecewise smooth initial value problems},
 keywords={interval methods, non-smooth systems, initial value problems},
}