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Persistence of attractors for one-step discretization of ordinary differential equations

Title data

Grüne, Lars:
Persistence of attractors for one-step discretization of ordinary differential equations.
In: IMA Journal of Numerical Analysis. Vol. 21 (July 2001) Issue 3 . - pp. 751-767.
ISSN 1464-3642
DOI: https://doi.org/10.1093/imanum/21.3.751

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Abstract in another language

We consider numerical one-step approximations of ordinary differential equations and present two results on the persistence of attractors appearing in the numerical system.First, we show that the upper limit of a sequence of numerical attractors for a sequence of vanishing time step is an attractor for the approximated system if and only if for all these time steps the numerical one-step schemes admit attracting sets which approximate this upper limit set and attract with a uniform rate. Second, we show that if these numerical attractors themselves attract with a uniformly rate, then they converge to some set if and only if this set is an attractor for the approximated system. In this case, we can also give an estimate for the rate of convergence depending on the rate of attraction and on the order of the numerical scheme.

Further data

Item Type: Article in a journal
Refereed: Yes
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 > 510 Mathematics
Date Deposited: 23 Feb 2021 09:09
Last Modified: 11 May 2021 11:17
URI: https://eref.uni-bayreuth.de/id/eprint/63322