## 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 |