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Selection Strategies for Set-Valued Runge-Kutta Methods

Title data

Baier, Robert:
Selection Strategies for Set-Valued Runge-Kutta Methods.
In: Li, Zhilin ; Vulkov, Lubin ; Waśniewski, Jerzy (ed.): Numerical Analysis and Its Applications : Third International Conference, NAA 2004, Rousse, Bulgaria, June 29-July 3, 2004 ; Revised Selected Papers. - Berlin ; Heidelberg : Springer , 2005 . - pp. 149-157 . - (Lecture Notes in Computer Science ; 3401 )
ISBN 978-3-540-24937-5
DOI: https://doi.org/10.1007/978-3-540-31852-1_16

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Abstract in another language

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: Article in a book
Refereed: Yes
Additional notes: Contents:
1. Introduction
2. Quadrature and Combination Methods
3. Set-Valued Runge-Kutta Methods
4. Conclusions
Keywords: Set-valued Runge-Kutta methods; Linear differential inclusions; Selection strategies; Modified Euler
Subject classification: Mathematics Subject Classification Code: 65L05 (65L06 34A30)
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)
Result of work at the UBT: Yes
DDC Subjects: 500 Science
500 Science > 510 Mathematics
Date Deposited: 02 Mar 2021 09:16
Last Modified: 14 May 2021 09:25
URI: https://eref.uni-bayreuth.de/id/eprint/63548