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Matem. Mod., 2017, Volume 29, Number 1, Pages 3–19 (Mi mm3803)  

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

On implicit Runge–Kutta methods received as a result of inversion of explicit methods

L. M. Skvortsov

Bauman Moscow State Technical University

Abstract: Inverse methods for explicit Runge–Kutta methods are considered. Such methods have a number of advantages, but their drawback is the low (1st) stage order. It leads to reduction of real order when solving stiff and differential-algebraic equations. The new methods possessing properties of methods of higher stage order are offered. Results of numerical experiments show that the offered methods allow us to avoid an order reduction.

Keywords: inverse Runge–Kutta methods, stiff equations, differential-algebraic equations, order reduction phenomenon.

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English version:
Mathematical Models and Computer Simulations, 2017, 9:4, 498–510

Received: 26.11.2015

Citation: L. M. Skvortsov, “On implicit Runge–Kutta methods received as a result of inversion of explicit methods”, Matem. Mod., 29:1 (2017), 3–19; Math. Models Comput. Simul., 9:4 (2017), 498–510

Citation in format AMSBIB
\Bibitem{Skv17}
\by L.~M.~Skvortsov
\paper On implicit Runge--Kutta methods received as a result of inversion of explicit methods
\jour Matem. Mod.
\yr 2017
\vol 29
\issue 1
\pages 3--19
\mathnet{http://mi.mathnet.ru/mm3803}
\elib{https://elibrary.ru/item.asp?id=28405089}
\transl
\jour Math. Models Comput. Simul.
\yr 2017
\vol 9
\issue 4
\pages 498--510
\crossref{https://doi.org/10.1134/S2070048217040123}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85024391417}


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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
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