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Difference Methods for Differential Inclusions : A Survey

Title data

Dontchev, Asen ; Lempio, Frank:
Difference Methods for Differential Inclusions : A Survey.
In: SIAM Review. Vol. 34 (November 1992) Issue 2 . - pp. 263-294.
ISSN 1095-7200
DOI: https://doi.org/10.1137/1034050

Review:

Abstract in another language

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.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: convergence of numerical methods; difference equations; difference methods; differential inclusions; mathematical techniques; oscillating systems; vehicle dynamics
Subject classification: Mathematics Subject Classification Code: 34A60 (34A50 49J24 65L05)
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Former Professors
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Result of work at the UBT: Yes
DDC Subjects: 500 Science
500 Science > 510 Mathematics
Date Deposited: 16 Feb 2021 09:30
Last Modified: 23 Mar 2021 09:13
URI: https://eref.uni-bayreuth.de/id/eprint/63087