A verified method for solving piecewise smooth initial value problems

• Autorzy: Ekaterina Auer , Stefan Kiel , Andreas Rauh
• 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 VAL E NC IA-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 methods; non-smooth systems; initial value problems

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2013
• Tom: 23
• Numer: 4
• Strony: 731-747

Daty

wydano

2013

otrzymano

2012-12-05

poprawiono

2013-04-30

poprawiono

2013-06-19

Twórcy

autor

Ekaterina Auer

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

autor

Stefan Kiel

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

autor

Andreas Rauh

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

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Identyfikatory

DOI

10.2478/amcs-2013-0055