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Zh. Vychisl. Mat. Mat. Fiz., 2017, Volume 57, Number 7, Pages 1126–1141 (Mi zvmmf10586)  

This article is cited in 1 scientific paper (total in 1 paper)

How to avoid accuracy and order reduction in Runge–Kutta methods as applied to stiff problems

L. M. Skvortsov

Bauman State Technical University, Moscow, Russia

Abstract: The solution of stiff problems is frequently accompanied by a phenomenon known as order reduction. The reduction in the actual order can be avoided by applying methods with a fairly high stage order, ideally coinciding with the classical order. However, the stage order sometimes fails to be increased; moreover, this is not possible for explicit and diagonally implicit Runge–Kutta methods. An alternative approach is proposed that yields an effect similar to an increase in the stage order. New implicit and stabilized explicit Runge–Kutta methods are constructed that preserve their order when applied to stiff problems.

Key words: Runge–Kutta methods, stiff problems, order reduction.

DOI: https://doi.org/10.7868/S0044466917070134

Full text: PDF file (661 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2017, 57:7, 1124–1139

Bibliographic databases:

UDC: 519.62
Received: 17.09.2015
Revised: 17.10.2016

Citation: L. M. Skvortsov, “How to avoid accuracy and order reduction in Runge–Kutta methods as applied to stiff problems”, Zh. Vychisl. Mat. Mat. Fiz., 57:7 (2017), 1126–1141; Comput. Math. Math. Phys., 57:7 (2017), 1124–1139

Citation in format AMSBIB
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\by L.~M.~Skvortsov
\paper How to avoid accuracy and order reduction in Runge--Kutta methods as applied to stiff problems
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2017
\vol 57
\issue 7
\pages 1126--1141
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\crossref{https://doi.org/10.7868/S0044466917070134}
\elib{https://elibrary.ru/item.asp?id=29404221}
\transl
\jour Comput. Math. Math. Phys.
\yr 2017
\vol 57
\issue 7
\pages 1124--1139
\crossref{https://doi.org/10.1134/S0965542517070119}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000406766300005}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85026802907}


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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. L. M. Skvortsov, “Implicit Runge–Kutta methods with explicit internal stages”, Comput. Math. Math. Phys., 58:3 (2018), 307–321  mathnet  crossref  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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