Discrete approximations of differential inclusions
F. Lempio, V. M. Veliov:
Discrete approximations of differential inclusions
in:
Department of Mathematics, University of Bayreuth
(eds.)
Bayreuther Mathematische Schriften
54,
Bayreuth, Germany,
1998,
149 - 232
Smart-Link:
http://bms.math.uni-bayreuth.de/all_books.html#vol_54
ISBN/ISSN/ISMV Nummer: 0172-1062
MR Nummer:
1643941
Zentralblattnummer:
0922.65059
Keywords: differential inclusions; Runge-Kutta methods; discrete approximations; reachable sets; set-valued numerical analysis
Mathematics Subject Classification Code: 49M25 (34A60 49D25 65L05)
Abstract:
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.
Inhaltsverzeichnis:
1. | Introduction and Preliminaries |
2. | Approximation of Some Trajectory |
3. | Approximation of All Trajectories |
4. | Hausdorff Approximation of the Reachable Set |
5. | Connection with Optimal Control |