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Selection Strategies of Set-Valued Runge-Kutta Methods

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00005592
URN to cite this document: urn:nbn:de:bvb:703-epub-5592-9

Title data

Baier, Robert:
Selection Strategies of Set-Valued Runge-Kutta Methods.
Bayreuth , 2004

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Abstract

A general framework for proving an order of convergence for set-valued Runge Kutta methods is given in the case of linear differential inclusions, if the attainable set at a given time should be approximated. The set-valued method is interpreted as a (set-valued) quadrature method with disturbed values for the fundamental solution at the nodes of the quadrature method. If the precision of the quadrature method and the order of the disturbances fit together, then an overall order of convergence could be guaranteed. The framework is applied to several Runge-Kutta methods up to order 4 with different selections strategies, i.e. piecewise constant, piecewise linear, two and more independent choices. Several numerical examples are calculated and the corresponding attainable sets are shown.

Further data

Item Type: Working paper, discussion paper
Keywords: Set-valued Runge-Kutta methods; Selection strategies; Reachable sets; Linear differential inclusions
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)
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-5592-9
Date Deposited: 21 May 2021 07:06
Last Modified: 21 May 2021 07:06
URI: https://epub.uni-bayreuth.de/id/eprint/5592

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