Selection Strategies for Set-Valued Runge-Kutta Methods

Titelangaben

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

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).