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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2008, Volume 48, Number 3, Pages 418–429
(Mi zvmmf167)
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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
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
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
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https://www.mathnet.ru/eng/zvmmf167 https://www.mathnet.ru/eng/zvmmf/v48/i3/p418
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