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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2008, Volume 48, Number 11, Pages 2008–2018 (Mi zvmmf86)  
This article is cited in 8 scientific papers (total in 8 papers)

An efficient scheme for the implementation of implicit Runge–Kutta methods

L. M. Skvortsov

Bauman State Technical University, Vtoraya Baumanskaya ul. 5, Moscow, 107005, Russia
Full-text PDF (1288 kB) Citations (8)
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Abstract: A scheme is proposed for solving nonlinear algebraic equations arising in the implementation of the implicit Runge–Kutta methods. In contrast to the available schemes, not only the starting values of the variables but also those of the derivatives are predicted. This makes it possible to reduce the number of evaluations of the function (the right-hand side) at each implicit stage without significantly reducing the accuracy of integration.
Key words: implicit Runge–Kutta methods, modified Newton's iteration, starting values, stiffness.
Received: 12.04.2008
English version:
Computational Mathematics and Mathematical Physics, 2008, Volume 48, Issue 11, Pages 2007–2017
DOI: https://doi.org/10.1134/S0965542508110092
Bibliographic databases:
Document Type: Article
UDC: 519.622
Language: Russian
Citation: L. M. Skvortsov, “An efficient scheme for the implementation of implicit Runge–Kutta methods”, Zh. Vychisl. Mat. Mat. Fiz., 48:11 (2008), 2008–2018; Comput. Math. Math. Phys., 48:11 (2008), 2007–2017
Citation in format AMSBIB
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    Abstract page:563
    Full-text PDF :220
    References:54
    First page:13
     
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