Object
Title: A verified method for solving piecewise smooth initial value problems
Contributor:
Korbicz, Józef (1951- ) - red. ; Uciński, Dariusz - red.
Group publication title:
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. ; 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.
Publisher:
Zielona Góra: Uniwersytet Zielonogórski
Resource Identifier:
DOI:
Pages:
Source:
AMCS, volume 23, number 4 (2013) ; click here to follow the link
Language:
Rights:
Biblioteka Uniwersytetu Zielonogórskiego
Object collections:
- Digital Library of Zielona Góra > Repository > Faculties > Faculty of Computer, Electrical and Control Engineering
- Digital Library of Zielona Góra > Repository > Types of work > Articles
- Digital Library of Zielona Góra > Repository > Scientific journals and UZ publishing series > International Journal of Applied Mathematics and Computer Science (AMCS) > International Journal of Applied Mathematics and Computer Science (AMCS) (2013)
Last modified:
Nov 5, 2024
In our library since:
Apr 23, 2024
Number of object content hits:
51
All available object's versions:
https://zbc.uz.zgora.pl/publication/88694
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International Journal of Applied Mathematics and Computer Science (AMCS)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 26 (2016)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 25 (2015)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 24 (2014)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 23 (2013)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 23, number 1 (2013)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 23, number 2 (2013)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 23, number 3 (2013)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 23, number 4 (2013)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 21 (2011)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 9 (1999)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 26 (2016)
| Edition name | Date |
|---|---|
| A verified method for solving piecewise smooth initial value problems | Nov 5, 2024 |
