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Dontchev, Asen ; Lempio, Frank:
Difference Methods for Differential Inclusions : A Survey.
In: SIAM Review.
Bd. 34
(1992)
Heft 2
.
- S. 263-294.
ISSN 1095-7200
DOI: https://doi.org/10.1137/1034050
| Rez.: |
Abstract
The main objective of this survey is to study convergence properties of difference methods applied to differential inclusions. It presents, in a unified way, a number of results scattered in the literature and provides also an introduction to the topic.
Convergence proofs for the classical Euler method and for a class of multistep methods are outlined. It is shown how numerical methods for stiff differential equations can be adapted to differential inclusions with additional monotonicity properties. Together with suitable localization procedures, this approach results in higher-order methods.
Convergence properties of difference methods with selection strategies are investigated, especially strate- gies forcing convergence to solutions with additional smoothness properties.
The error of the Euler method, represented by the Hausdorff distance between the set of approximate solutions and the set of exact solutions is estimated. First- and second-order approximations to the reachable sets are presented.
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| Publikationsform: | Artikel in einer Zeitschrift |
|---|---|
| Begutachteter Beitrag: | Ja |
| Keywords: | convergence of numerical methods; difference equations; difference methods; differential inclusions; mathematical techniques; oscillating systems; vehicle dynamics |
| Fachklassifikationen: | Mathematics Subject Classification Code: 34A60 (34A50 49J24 65L05) |
| Institutionen der Universität: | Fakultäten Fakultäten > Fakultät für Mathematik, Physik und Informatik Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Ehemalige Professoren Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik V (Angewandte Mathematik) |
| Titel an der UBT entstanden: | Ja |
| Themengebiete aus DDC: | 500 Naturwissenschaften und Mathematik 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Eingestellt am: | 16 Feb 2021 09:30 |
| Letzte Änderung: | 24 Jan 2022 10:02 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/63087 |