A verified method for solving piecewise smooth initial value problems

• Autorzy: Auer E. , Kiel S. , Rauh A.
• Języki publikacji: EN

Abstrakty

EN

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. 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. 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.

Słowa kluczowe

EN

interval method; non smooth system; initial value problem

PL

metoda przedziałowa; metoda nie gładka; zagadnienie początkowe

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2013
• Tom: Vol. 23, no. 4
• Strony: 731--747
• Opis fizyczny: Bibliogr. 50 poz., tab., wykr.

Twórcy

autor

Auer E.

• Department of Computer Science and Applied Cognitive Science, University of Duisburg–Essen, 47048 Duisburg, Germany

autor

Kiel S.

• Department of Computer Science and Applied Cognitive Science, University of Duisburg–Essen, 47048 Duisburg, Germany

autor

Rauh A.

• Chair of Mechatronics, University of Rostock, Justus-von-Liebig-Weg 6, 18059 Rostock, Germany

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