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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2008, Volume 48, Number 9, Pages 1580–1606 (Mi zvmmf109)  
This article is cited in 3 scientific papers (total in 3 papers)

Automatic step size and order control in implicit one-step extrapolation methods

G. Yu. Kulikova, E. Y. Khrustalevab

a School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa
b Faculty of Mathematics and Mechanics, Ul'yanovsk State University, ul. L. Tolstogo 42, Ul'yanovsk, 432970, Russia
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Abstract: A theory is presented for implicit one-step extrapolation methods for ordinary differential equations. The computational schemes used in such methods are based on the implicit Runge–Kutta methods. An efficient implementation of implicit extrapolation is based on the combined step size and order control. The emphasis is placed on calculating and controlling the global error of the numerical solution. The aim is to achieve the user-prescribed accuracy in an automatic mode (ignoring round-off errors). All the theoretical conclusions of this paper are supported by the numerical results obtained for test problems.
Key words: implicit one-step extrapolation methods, automatic step size control, control of the order in one-step methods, Runge–Kutta method.
Received: 31.05.2007
Revised: 20.12.2007
English version:
Computational Mathematics and Mathematical Physics, 2008, Volume 48, Issue 9, Pages 1545–1569
DOI: https://doi.org/10.1134/S0965542508090066
Bibliographic databases:
Document Type: Article
UDC: 519.622
Language: Russian
Citation: G. Yu. Kulikov, E. Y. Khrustaleva, “Automatic step size and order control in implicit one-step extrapolation methods”, Zh. Vychisl. Mat. Mat. Fiz., 48:9 (2008), 1580–1606; Comput. Math. Math. Phys., 48:9 (2008), 1545–1569
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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