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Discrete Filippov-type stability for one-sided Lipschitzian difference inclusions

URN zum Zitieren dieses Dokuments: urn:nbn:de:bvb:703-epub-3402-0

Titelangaben

Baier, Robert ; Farkhi, Elza:
Discrete Filippov-type stability for one-sided Lipschitzian difference inclusions.
Mathematisches Institut, Universität Bayreuth; School of Mathematical Sciences, Tel Aviv University
Bayreuth ; Tel Aviv , 2017 . - 24 S.

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Projektfinanzierung: Andere
The Hermann Minkowski Center for Geometry at Tel Aviv University, Israel

Abstract

We state and prove Filippov-type stability theorems for discrete difference inclusions obtained by the Euler discretization of a differential inclusion with perturbations in the set of initial points, in the right-hand side and in the state variable. We study the cases in which the right-hand side of the inclusion is not necessarily Lipschitz, but satisfies a weaker one-sided Lipschitz (OSL) or strengthened one-sided Lipschitz (SOSL) condition. The obtained estimates imply stability of the discrete solutions for infinite number of fixed time steps if the OSL constant is negative and the perturbations are bounded in certain norms. We show a better order of stability for SOSL right-hand sides and apply our theorems to estimate the distance from the solutions of other difference methods, as for the implicit Euler scheme to the set of solutions of the Euler scheme. We also prove a discrete relaxation stability theorem for the considered difference inclusion, which also extends a theorem of G. Grammel (2003) from the class of Lipschitz maps to the wider class of OSL ones.

Weitere Angaben

Publikationsform: Preprint, Postprint, Working paper, Diskussionspapier
Zusätzliche Informationen (öffentlich sichtbar): Accepted for publication in Lecture Notes in Economics and Mathematical Systems.
Dedicated to Vladimir Veliov's 65-th birthday.

Contents:
1. Introduction
2. Problem and Preliminaries
2.1 Preliminaries
2.2 Basic assumptions
3. Discrete Filippov-Type Theorems for One-Sided Lipschitz Maps
3.1 Outer perturbations
3.2 Inner perturbations
3.3 Both perturbations and applications
3.4 Discrete relaxation stability theorem
4. Discrete Filippov-Type Theorems for Strengthened One-Sided Lipschitz Maps
4.1 Both perturbations
4.2 Application
Keywords: one-sided Lipschitz condition; strengthened one-sided Lipschitz condition; set-valued Euler’s method; differential inclusions
Fachklassifikationen: Mathematics Subject Classification Code: 34A60 47H05 (39A30 54C60)
Themengebiete aus DDC: 500 Naturwissenschaften und Mathematik > 510 Mathematik
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 > Lehrstuhl Mathematik V (Angewandte Mathematik)
Profilfelder
Profilfelder > Advanced Fields
Profilfelder > Advanced Fields > Nichtlineare Dynamik
Sprache: Englisch
Titel an der UBT entstanden: Ja
URN: urn:nbn:de:bvb:703-epub-3402-0
Eingestellt am: 13 Okt 2017 05:44
Letzte Änderung: 13 Okt 2017 05:44
URI: https://epub.uni-bayreuth.de/id/eprint/3402

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