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Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 3, Pages 326–339 (Mi zvmmf10686)  

Implicit Runge–Kutta methods with explicit internal stages

L. M. Skvortsov

Bauman Moscow State Technical University, Moscow, Russia

Abstract: The main computational costs of implicit Runge–Kutta methods are caused by solving a system of algebraic equations at every step. By introducing explicit stages, it is possible to increase the stage (or pseudo-stage) order of the method, which makes it possible to increase the accuracy and avoid reducing the order in solving stiff problems, without additional costs of solving algebraic equations. The paper presents implicit methods with an explicit first stage and one or two explicit internal stages. The results of solving test problems are compared with similar methods having no explicit internal stages.

Key words: implicit Runge–Kutta methods, stiff problems, differential-algebraic problems, order reduction, stage order, pseudo-stage order.

DOI: https://doi.org/10.7868/S004446691803002X

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English version:
Computational Mathematics and Mathematical Physics, 2018, 58:3, 307–321

Bibliographic databases:

UDC: 519.62
Received: 12.09.2016

Citation: L. M. Skvortsov, “Implicit Runge–Kutta methods with explicit internal stages”, Zh. Vychisl. Mat. Mat. Fiz., 58:3 (2018), 326–339; Comput. Math. Math. Phys., 58:3 (2018), 307–321

Citation in format AMSBIB
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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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