Title data
Baier, Robert ; Farkhi, Elza:
Discrete Filippovtype stability for onesided Lipschitzian difference inclusions.
Mathematisches Institut, Universität Bayreuth, School of Mathematical Sciences, Tel Aviv University
Bayreuth ; Tel Aviv
,
2017
.  24 S.


Download (366kB)

Project information
Project financing: 
Andere The Hermann Minkowski Center for Geometry at Tel Aviv University, Israel 

Abstract
We state and prove Filippovtype 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 righthand side and in the state variable. We study the cases in which the righthand side of the inclusion is not necessarily Lipschitz, but satisfies a weaker onesided Lipschitz (OSL) or strengthened onesided 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 righthand 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.
Further data
Item Type:  Preprint, postprint 

Additional notes (visible to public):  Accepted for publication in Lecture Notes in Economics and Mathematical Systems.
Dedicated to Vladimir Veliov's 65th birthday. Contents: 1. Introduction 2. Problem and Preliminaries 2.1 Preliminaries 2.2 Basic assumptions 3. Discrete FilippovType Theorems for OneSided Lipschitz Maps 3.1 Outer perturbations 3.2 Inner perturbations 3.3 Both perturbations and applications 3.4 Discrete relaxation stability theorem 4. Discrete FilippovType Theorems for Strengthened OneSided Lipschitz Maps 4.1 Both perturbations 4.2 Application 
Keywords:  onesided Lipschitz condition; strengthened onesided Lipschitz condition; setvalued Euler’s method; differential inclusions 
Subject classification:  Mathematics Subject Classification Code: 34A60 47H05 (39A30 54C60) 
DDC Subjects:  500 Science > 510 Mathematics 
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 > Chair Mathematics V (Applied Mathematics) Profile Fields Profile Fields > Advanced Fields Profile Fields > Advanced Fields > Nonlinear Dynamics 
Language:  English 
Originates at UBT:  Yes 
URN:  urn:nbn:de:bvb:703epub34020 
Date Deposited:  13 Oct 2017 05:44 
Last Modified:  28 Mar 2019 10:20 
URI:  https://epub.unibayreuth.de/id/eprint/3402 