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

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00005484
URN to cite this document: urn:nbn:de:bvb:703-epub-5484-4

Title data

Grüne, Lars:
Persistence of attractors for one-step discretization of ordinary differential equations.
Bayreuth , 1999

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Abstract

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:	Preprint, postprint
Additional notes (visible to public):	erschienen In: IMA Journal of Numerical Analysis. Bd. 21 (Juli 2001) Heft 3 . - S. 751-767
Keywords:	ordinary differential equation; numerical one-step approximation; attractor; dynamical system
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-5484-4
Date Deposited:	11 May 2021 11:16
Last Modified:	11 May 2021 11:17
URI:	https://epub.uni-bayreuth.de/id/eprint/5484

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