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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2008, Volume 48, Number 3, Pages 418–429 (Mi zvmmf167)  
This article is cited in 16 scientific papers (total in 16 papers)

Optimal first- to sixth-order accurate Runge–Kutta schemes

E. A. Alshinaa, E. M. Zaksb, N. N. Kalitkina

a Institute of Mathematical Modeling, Russian Academy of Sciences, Miusskaya pl. 4a, Moscow, 125047, Russia
b Moscow State Institute of Electronic Engineering (Technical University), Zelenograd, Moscow, 124498, Russia
Full-text PDF (1437 kB) Citations (16)
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Abstract: An optimal choice of free parameters in explicit Runge–Kutta schemes up to the sixth order is discussed. A sixth-order seven-stage scheme that is immediately ahead of Butcher's second barrier is constructed. The study is performed in the most general form, and its results are applicable to both autonomous and nonautonomous problems.
Key words: optimal Runge–Kutta schemes, Cauchy problems for ordinary differential equations, sixth-order seven-stage scheme.
Received: 05.09.2007
English version:
Computational Mathematics and Mathematical Physics, 2008, Volume 48, Issue 3, Pages 395–405
DOI: https://doi.org/10.1134/S0965542508030068
Bibliographic databases:
Document Type: Article
UDC: 519.624
Language: Russian
Citation: E. A. Alshina, E. M. Zaks, N. N. Kalitkin, “Optimal first- to sixth-order accurate Runge–Kutta schemes”, Zh. Vychisl. Mat. Mat. Fiz., 48:3 (2008), 418–429; Comput. Math. Math. Phys., 48:3 (2008), 395–405
Citation in format AMSBIB
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    • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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