Creator:
Auer, Ekaterina ; Kiel, Stefan ; Rauh, Andreas
Contributor:
Korbicz, Józef - red. ; Uciński, Dariusz - red.
Title:
A verified method for solving piecewise smooth initial value problems
Group publication title:
Subject and Keywords:
interval methods ; non-smooth systems ; initial value problems
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
Date:
Resource Type:
DOI:
Pages:
Source:
AMCS, volume 23, number 4 (2013) ; click here to follow the link