Korbicz, Józef - red. ; Uciński, Dariusz - red.
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.
Zielona Góra: Uniwersytet Zielonogórski
AMCS, volume 23, number 4 (2013) ; click here to follow the link
Biblioteka Uniwersytetu Zielonogórskiego
Apr 23, 2024
Apr 23, 2024
23
https://zbc.uz.zgora.pl/repozytorium/publication/88694
Edition name | Date |
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A verified method for solving piecewise smooth initial value problems | Apr 23, 2024 |
Luo, Na Tan, Yonghong Dong, Ruili Iacono, Mauro - ed. Kołodziej, Joanna - ed.
Auer, Ekaterina Luther, Wolfram Rauh, Andreas - ed. Auer, Ekaterina - ed. Hofer,Eberhard P. - ed. Luther, Wolfram - ed.
Rauh, Andreas Brill, Michael Günther, Clemens Rauh, Andreas - ed. Auer, Ekaterina - ed. Hofer,Eberhard P. - ed. Luther, Wolfram - ed.
Rauh, Andreas Minisini, Johanna Hofer, Eberhard P. Rauh, Andreas - ed. Auer, Ekaterina - ed. Hofer,Eberhard P. - ed. Luther, Wolfram - ed.
Rauh, Andreas Butt, Saif S. Aschemann, Harald Korbicz, Józef - red. Uciński, Dariusz - red.
Rauh, Andreas Senkel, Luise Aschemann, Harald Saurin, Vasily V. Kostin, Georgy V. Korbicz, Józef - red. Uciński, Dariusz - red.