## Title data

Lempio, Frank:

**Modified Euler methods for differential inclusions.**

*In:* Kurzanskij, Aleksandr B. ; Veliov, Vladimir M.
(ed.):
Set-Valued Analysis and Differential Inclusions : A Collection of Papers resulting from a Workshop held in Pamporovo, Bulgaria, September 17-21, 1990. -
Basel
: Birkhäuser
,
1993
. - pp. 131-148
. - (Progress in Systems and Control Theory
; 16
)

ISBN 978-3-7643-3733-9

Review: |

## Abstract in another language

Classical Euler method and simple modifications like the method of Euler-Cauchy, improved Euler method and implicit midpoint rule are discussed with regard to the approximate solution of differential inclusions.

Numerical tests suggest first order convergence of Euler's method at least for specially structured right-hand sides even if the usual Lipschitz condition does not hold. The basic idea of the proof of this convergence property is sketched using a strengthened one-sided Lipschitz condition.

Other reduction for methods which are of higher order for single-valued sufficiently smooth right-hand sides is exemplified numerically for improved Euler method and implicit midpoint rule. Typical advantages of implicit midpoint rule are discussed.

## Further data

Item Type: | Article in a book |
---|---|

Refereed: | Yes |

Subject classification: | Mathematics Subject Classification Code: 34A45 (34A60 65L05 65L99) |

Institutions of the University: | Faculties 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) |

Result of work at the UBT: | Yes |

DDC Subjects: | 500 Science 500 Science > 510 Mathematics |

Date Deposited: | 17 Feb 2021 07:49 |

Last Modified: | 23 Mar 2021 09:13 |

URI: | https://eref.uni-bayreuth.de/id/eprint/63092 |