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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Vydané v:	Numerical analysis and applications Ročník 4; číslo 3; s. 199 - 209
Hlavní autori:	Kulikov, G. Yu, Kuznetsov, E. B., Khrustaleva, E. Yu
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Dordrecht SP MAIK Nauka/Interperiodica 01.07.2011
Predmet:	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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Popis
Shrnutí:	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