## Title data

Grüne, Lars:

**Attraction Rates, Robustness, and Discretization of Attractors.**

*In:* SIAM Journal on Numerical Analysis.
Vol. 41
(July 2003)
Issue 6
.
- pp. 2096-2113.

ISSN 1095-7170

DOI: https://doi.org/10.1137/S003614290139411X

## Abstract in another language

We investigate necessary and sufficient conditions for the convergence of attractors of discrete time dynamical systems induced by numerical one-step approximations of ordinary differential equations (ODEs) to an attractor for the approximated ODE. We show that both the existence of uniform attraction rates (i.e., uniform speed of convergence towards the attractors) and uniform robustness with respect to perturbations of the numerical attractors are necessary and sufficient for this convergence property. In addition, we can conclude estimates for the rate of convergence in the Hausdorff metric.

## Further data

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

Refereed: | Yes |

Keywords: | Numerical one-step approximation; Attractor; Attraction rate; Robustness; Convergence; Discrete time dynamical systems |

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 > Chair Mathematics V (Applied Mathematics) 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 |

Result of work at the UBT: | No |

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

Date Deposited: | 01 Mar 2021 14:52 |

Last Modified: | 23 Mar 2021 09:13 |

URI: | https://eref.uni-bayreuth.de/id/eprint/63458 |