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Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 5, Pages 755–765 (Mi zvmmf10030)  

This article is cited in 3 scientific papers (total in 3 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.

DOI: https://doi.org/10.7868/S0044466914050160

Full text: PDF file (332 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2014, 54:5, 775–784

Bibliographic databases:

UDC: 519.622
Received: 05.06.2013

Citation: L. M. Skvortsov, “Singly implicit diagonally extended Runge–Kutta methods of fourth order”, Zh. Vychisl. Mat. Mat. Fiz., 54:5 (2014), 755–765; Comput. Math. Math. Phys., 54:5 (2014), 775–784

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. G. Yu. Kulikov, “Embedded symmetric nested implicit Runge–Kutta methods of Gauss and Lobatto types for solving stiff ordinary differential equations and Hamiltonian systems”, Comput. Math. Math. Phys., 55:6 (2015), 983–1003  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. L. M. Skvortsov, “How to avoid accuracy and order reduction in Runge–Kutta methods as applied to stiff problems”, Comput. Math. Math. Phys., 57:7 (2017), 1124–1139  mathnet  crossref  crossref  isi  elib
    3. X. Piao, S. Bu, D. Kim, Ph. Kim, “An embedded formula of the Chebyshev collocation method for stiff problems”, J. Comput. Phys., 351 (2017), 376–391  crossref  mathscinet  zmath  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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