# 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 |