Selection Strategies for Set-Valued Runge-Kutta Methods

R. Baier: Selection Strategies for Set-Valued Runge-Kutta Methods
in: Proceedings of the Numerical Analysis and Its Applications (NAA 2004), Third International Conference, Rousse, Bulgaria, June 29 - July 3, 2004, Revised Selected Papers, Z. Li, L.G. Vulkov, J. Wasniewski (eds.)
Lecture Notes in Computer Science 3401, Springer Verlag, Berlin-Heidelberg, 2005, 149 - 157

DOI: 10.1007/b106395
Zentralblattnummer: 1118.65342
Keywords: set-valued Runge-Kutta methods; linear differential inclusions; selection strategies; modified Euler
Mathematics Subject Classification Code: 65L05 (65L06 34A30)
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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).

Contents:

1. Introduction
2. Quadrature and Combination Methods
3. Set-Valued Runge-Kutta Methods
4. Conclusions

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