Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zh. Vychisl. Mat. Mat. Fiz.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 5, Pages 746–754 (Mi zvmmf10029)  

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

Estimating the error in the classical Runge–Kutta methods

S. I. Khashin

Ivanovo State University, ul. Ermaka 39, Ivanovo, 153025, Russia

Abstract: It is well known that it is impossible to construct embedded firth-order methods for estimating the error in four-stage Runge–Kutta methods of order four. In this paper, a technique for error estimating with no additional calculations of the right-hand sides of equations is proposed. The proposed estimate is of fifth order and is based on the data provided by three successive steps of the method. The main results of the paper are formulas for evaluating the local error based on two and three steps of the method, respectively. The main conclusion of the paper is that an automatic stepsize control should not necessarily be based on embedded methods. Such a control can be implemented for an arbitrary method.

Key words: Runge–Kutta methods, estimate of the local error.

DOI: https://doi.org/10.7868/S0044466914050172

Full text: PDF file (176 kB)
References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2014, 54:5, 767–774

Bibliographic databases:

UDC: 519.622
Received: 30.08.2013
Revised: 09.12.2013

Citation: S. I. Khashin, “Estimating the error in the classical Runge–Kutta methods”, Zh. Vychisl. Mat. Mat. Fiz., 54:5 (2014), 746–754; Comput. Math. Math. Phys., 54:5 (2014), 767–774

Citation in format AMSBIB
\Bibitem{Kha14}
\by S.~I.~Khashin
\paper Estimating the error in the classical Runge--Kutta methods
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2014
\vol 54
\issue 5
\pages 746--754
\mathnet{http://mi.mathnet.ru/zvmmf10029}
\crossref{https://doi.org/10.7868/S0044466914050172}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3211880}
\elib{https://elibrary.ru/item.asp?id=21418165}
\transl
\jour Comput. Math. Math. Phys.
\yr 2014
\vol 54
\issue 5
\pages 767--774
\crossref{https://doi.org/10.1134/S0965542514050145}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000336450500004}
\elib{https://elibrary.ru/item.asp?id=24048837}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84901634210}


Linking options:
  • http://mi.mathnet.ru/eng/zvmmf10029
  • http://mi.mathnet.ru/eng/zvmmf/v54/i5/p746

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. Hippolyte Séka, Kouassi Richard  Assui, “Order of the Runge-Kutta method and evolution of the stability region”, Ural Math. J., 5:2 (2019), 64–71  mathnet  crossref  mathscinet  zmath
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
    Number of views:
    This page:1048
    Full text:427
    References:69
    First page:35

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2022