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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2011, Volume 14, Number 3, Pages 245–259 (Mi sjvm439)  
This article is cited in 4 scientific papers (total in 4 papers)

On the global error control in nested implicit Runge–Kutta methods of Gauss type

G. Yu. Kulikova, E. B. Kuznetsovb, E. Yu. Khrustalevac

a CEMAT, Instituto Superior Técnico, TU Lisbon, Lisboa, Portugal
b Moscow Aviation Institute (State University of Aerospace Technologies), Moscow
c Ulyanovsk State University, Faculty of Mathematics and Information Technologies, Ulyanovsk
Full-text PDF (282 kB) Citations (4)
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Abstract: The automatic global error control based on a combined step size and order control presented by Kulikov and Khrustaleva in 2008 is investigated. A special attention is given to the efficiency of computation because the implicit extrapolation based on the multi-stage implicit Runge–Kutta schemes might be expensive. Especially, we discuss the technique of global error estimation and control in order to compute the numerical solution satisfying the user-supplied accuracy conditions (in exact arithmetic) in the automatic mode. The theoretical results of this paper are confirmed by numerical experiments on test problems.
Key words: implicit Runge–Kutta formulas, effective implementation, nested implicit schemes of Gauss type, global error estimation and control.
Received: 09.12.2010
English version:
Numerical Analysis and Applications, 2011, Volume 4, Issue 3, Pages 199–209
DOI: https://doi.org/10.1134/S1995423911030025
Bibliographic databases:
Document Type: Article
UDC: 519.622
Language: Russian
Citation: G. Yu. Kulikov, E. B. Kuznetsov, E. Yu. Khrustaleva, “On the global error control in nested implicit Runge–Kutta methods of Gauss type”, Sib. Zh. Vychisl. Mat., 14:3 (2011), 245–259; Num. Anal. Appl., 4:3 (2011), 199–209
Citation in format AMSBIB
\Bibitem{KulKuzKhr11}
\by G.~Yu.~Kulikov, E.~B.~Kuznetsov, E.~Yu.~Khrustaleva
\paper On the global error control in nested implicit Runge--Kutta methods of Gauss type
\jour Sib. Zh. Vychisl. Mat.
\yr 2011
\vol 14
\issue 3
\pages 245--259
\mathnet{http://mi.mathnet.ru/sjvm439}
\transl
\jour Num. Anal. Appl.
\yr 2011
\vol 4
\issue 3
\pages 199--209
\crossref{https://doi.org/10.1134/S1995423911030025}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79960820322}
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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