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Convergence Analysis for Selection Strategies of Set-Valued Runge-Kutta Methods

Title data

Baier, Robert:
Convergence Analysis for Selection Strategies of Set-Valued Runge-Kutta Methods.
Bayreuth : Mathematisches Institut , 2004 . - 40 S. - (Technical Report )

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 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
Subject classification: Mathematics Subject Classification Code: 65L06 (54C65 65L05 93B03 34A60)
Institutions of the University: 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
Result of work at the UBT: Yes
DDC Subjects: 500 Science
500 Science > 510 Mathematics
Date Deposited: 02 Mar 2021 08:09
Last Modified: 23 Mar 2021 09:13
URI: https://eref.uni-bayreuth.de/id/eprint/63486