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Selection Strategies for Set-Valued Runge-Kutta Methods

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00005509
URN to cite this document: urn:nbn:de:bvb:703-epub-5509-8

Title data

Baier, Robert:
Selection Strategies for Set-Valued Runge-Kutta Methods.
Bayreuth , 2005

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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 results are applied to modified Euler method to emphasize the dependence on a suitable selection strategy (one strategy leads to an order breakdown).

Further data

Item Type: Preprint, postprint
Additional notes (visible to public): Erscheint in: Li, Zhilin ; Vulkov, Lubin ; Waśniewski, Jerzy (Hrsg.): Numerical Analysis and Its Applications : Third International Conference, NAA 2004, Rousse, Bulgaria, June 29-July 3, 2004 ; Revised Selected Papers. - Berlin ; Heidelberg : Springer , 2005 . - S. 149-157
Keywords: Set-valued Runge-Kutta methods; Linear differential inclusions; Selection strategies; Modified Euler
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-5509-8
Date Deposited: 14 May 2021 09:24
Last Modified: 18 Jun 2021 07:56
URI: https://epub.uni-bayreuth.de/id/eprint/5509

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