## Title data

Karafyllis, Iasson ; Grüne, Lars:

**Feedback Stabilization Methods for the Numerical Solution of Systems of Ordinary Differential Equations.**

*In:*
Numerical analysis and applied mathematics : International Conference on Numerical Analysis and Applied Mathematics 2009. -
Melville, NY
: American Inst. of Physics
,
2009
. - pp. 152-155
. - (AIP Conference Proceedings
; 1168
)

ISBN 978-0-7354-0709-1

DOI: https://doi.org/10.1063/1.3241391

## Abstract in another language

In this work we study the problem of step size selection for numerical schemes, which guarantees that the numerical solution presents the same qualitative behavior as the original system of ordinary differential equations, by means of tools from nonlinear control theory. Lyapunov-based and Small-Gain feedback stabilization methods are presented for systems with a globally asymptotically stable equilibrium point. Proceeding this way, we derive conditions under which the step size selection problem is solvable (including a nonlinear generalization of the well-known A-stability property for the implicit Euler scheme) as well as step size selection strategies for several applications.

## Further data

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

Refereed: | Yes |

Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne 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 > Chair Mathematics V (Applied Mathematics) |

Result of work at the UBT: | Yes |

DDC Subjects: | 500 Science > 510 Mathematics |

Date Deposited: | 22 Feb 2021 13:48 |

Last Modified: | 23 Mar 2021 09:12 |

URI: | https://eref.uni-bayreuth.de/id/eprint/63345 |