On global error control in nested implicit Runge-Kutta methods of the gauss type

Automatic global error control based on a combined control of step size and order presented by Kulikov and Khrustaleva in 2008 is investigated. Special attention is given to the efficiency of computation, because the implicit extrapolation based on multistage implicit Runge-Kutta schemes may be expe...

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Veröffentlicht in:Numerical analysis and applications Jg. 4; H. 3; S. 199 - 209
Hauptverfasser: Kulikov, G. Yu, Kuznetsov, E. B., Khrustaleva, E. Yu
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Dordrecht SP MAIK Nauka/Interperiodica 01.07.2011
Schlagworte:
Mathematics
Mathematics and Statistics
Numerical Analysis
implicit Runge-Kutta formulas
efficient implementation
nested implicit schemes of the Gauss type
global error estimation and control
ISSN:1995-4239, 1995-4247
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Zusammenfassung:Automatic global error control based on a combined control of step size and order presented by Kulikov and Khrustaleva in 2008 is investigated. Special attention is given to the efficiency of computation, because the implicit extrapolation based on multistage implicit Runge-Kutta schemes may be expensive. Specifically, we discuss a technique of global error estimation and control in order to compute a numerical solution satisfying the user-supplied accuracy conditions (in exact arithmetic) automatically. The theoretical results of this paper are confirmed by numerical experiments on test problems.
ISSN:1995-4239
1995-4247
DOI:10.1134/S1995423911030025