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Sibirskii Zhurnal Vychislitel'noi Matematiki
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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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  • https://www.mathnet.ru/eng/sjvm/v14/i3/p245
    • This publication is cited in the following 4 articles:
    1. L. M. Skvortsov, “Implicit Runge–Kutta methods with explicit internal stages”, Comput. Math. Math. Phys., 58:3 (2018), 307–321  mathnet  crossref  crossref  isi  elib
    2. G. Yu. Kulikov, “Embedded symmetric nested implicit Runge–Kutta methods of Gauss and Lobatto types for solving stiff ordinary differential equations and Hamiltonian systems”, Comput. Math. Math. Phys., 55:6 (2015), 983–1003  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. V. N. Govorukhin, “On the choice of a method for integrating the equations of motion of a set of fluid particles”, Comput. Math. Math. Phys., 54:4 (2014), 706–718  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    4. L. M. Skvortsov, “Efficient implementation of second order implicit Runge–Kutta methods”, Math. Models Comput. Simul., 5:6 (2013), 565–574  mathnet  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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