This article is cited in 6 papers

Singly implicit diagonally extended Runge–Kutta methods of fourth order

L. M. Skvortsov

Bauman State Technical University, Vtoraya Baumanskaya ul. 5, Moscow, 105005, Russia

Abstract: Singly implicit diagonally extended Runge–Kutta methods make it possible to combine the merits of diagonally implicit methods (namely, the simplicity of implementation) and fully implicit ones (high stage order). Due to this combination, they can be very efficient at solving stiff and differential-algebraic problems. In this paper, fourth-order methods with an explicit first stage are examined. The methods have the third or fourth stage order. Consideration is given to an efficient implementation of these methods. The results of tests in which the proposed methods were compared with the fifth-order RADAU IIA method are presented.

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

UDC: 519.622

Received: 05.06.2013

DOI: 10.7868/S0044466914050160

 English version: Computational Mathematics and Mathematical Physics, 2014, 54:5, 775–784

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