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Discrete approximations of differential inclusions

Title data

Lempio, Frank ; Veliov, V. M.:
Discrete approximations of differential inclusions.
In: Bayreuther Mathematische Schriften. - Bayreuth : Math. Inst. der Univ. , 1998 . - pp. 149-232 . - (Bayreuther Mathematische Schriften ; 54 )

Review:

Abstract in another language

This paper is devoted to discretization methods for initial value problems for differential inclusions. Main emphasis is laid on set-valued analogues of Runge-Kutta methods.
The following questions are studied:
- Does every discrete trajectory approximate some exact solution, and with what accuracy?
- Is every exact solution approximated, and with what accuracy, by some discrete trajectory?
- What is the error between the discrete reachable set and the exact reachable set with respect to Hausdorff distance?
The material is presented as a survey, containing simultaneously a series of new results with complete proofs.

Further data

Item Type: Article in a book
Refereed: Yes
Keywords: Differential inclusions; Runge-Kutta methods; Discrete approximations; Reachable sets; Set-valued numerical analysis
Subject classification: Mathematics Subject Classification Code: 49M25 (34A60 49D25 65L05)
Institutions of the University: 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)
Faculties
Result of work at the UBT: Yes
DDC Subjects: 500 Science
500 Science > 510 Mathematics
Date Deposited: 24 Feb 2021 08:59
Last Modified: 08 Apr 2021 09:50
URI: https://eref.uni-bayreuth.de/id/eprint/63357