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Attraction Rates, Robustness, and Discretization of Attractors

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00005498
URN to cite this document: urn:nbn:de:bvb:703-epub-5498-7

Title data

Grüne, Lars:
Attraction Rates, Robustness, and Discretization of Attractors.
Bayreuth , 2001

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Abstract

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: Preprint, postprint
Additional notes (visible to public): Erscheint in: SIAM Journal on Numerical Analysis. Bd. 41 (Juli 2003) Heft 6 . - S. 2096-2113; https://doi.org/10.1137/S003614290139411X
Keywords: Numerical one-step approximation; Attractor; Attraction rate; Robustness; Convergence; Discrete time dynamical systems
DDC Subjects: 500 Science
500 Science > 510 Mathematics
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)
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-5498-7
Date Deposited: 12 May 2021 11:02
Last Modified: 21 Jun 2021 09:27
URI: https://epub.uni-bayreuth.de/id/eprint/5498

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