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Discrete Approximation of Impulsive Differential Inclusions

Title data

Baier, Robert ; Donchev, Tzanko:
Discrete Approximation of Impulsive Differential Inclusions.
In: Numerical Functional Analysis and Optimization. Vol. 31 (2010) Issue 6 . - pp. 653-678.
ISSN 1532-2467
DOI: https://doi.org/10.1080/01630563.2010.483878

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Abstract in another language

The paper deals with the approximation of the solution set and the reachable sets of an impulsive differential inclusion with variable times of impulses. It is strongly connected to T. Donchev, ``Approximation of the Solution Set of Impulsive Systems", Lecture Notes in Comput. Sci. 4818 (2008) and is its continuation. We achieve order of convergence 1 for the Euler approximation under Lipschitz assumptions on the set-valued right-hand side and on the functions describing the jump surfaces and jumps themselves. Another criterion prevents the beating phenomena and generalizes available conditions. Several test examples illustrate the conditions and the practical evaluation of the jump conditions.

Further data

Item Type: Article in a journal
Refereed: Yes
Additional notes: Contents:
1. Preliminaries
2. Approximation of the solution set
3. Approximation of the reachable set
Keywords: impulsive differential inclusions; numerical approximation of the solution set and the reachable set; Euler's method; convergence order; evaluation of the jump conditions
Subject classification: Mathematics Subject Classification Code: 34A37 (93B03 34A60 49M25)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 25 Feb 2021 08:24
Last Modified: 25 May 2021 13:16
URI: https://eref.uni-bayreuth.de/id/eprint/63445