L. M. Skvortsov, “Model equations for accuracy investigation of Runge–Kutta methods”, Mat. Model., 22:5 (2010), 146–160; Math. Models Comput. Simul., 2:6 (2010), 800

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Matematicheskoe modelirovanie, 2010, Volume 22, Number 5, Pages 146–160 (Mi mm2980)

This article is cited in 8 scientific papers (total in 8 papers)

Model equations for accuracy investigation of Runge–Kutta methods

L. M. Skvortsov

Bauman Moscow State Technical University

Full-text PDF (263 kB) Citations (8)

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Abstract: The simplest equations are considered that simulate the behavior of various error components of Runge–Kutta methods. The expressions for the local and global errors are obtained. The minimization of these errors allows one to construct explicit and implicit methods that have an improved accuracy when solving stiff and differential-algebraic problems.

Keywords: Runge–Kutta methods, still problems, differential-algebraic problems, order reduction phenomen.

Received: 16.04.2009

English version:
Mathematical Models and Computer Simulations, 2010, Volume 2, Issue 6, Pages 800–811
DOI: https://doi.org/10.1134/S2070048210060165

Bibliographic databases:

Document Type: Article

UDC: 519.622

Language: Russian

Citation: L. M. Skvortsov, “Model equations for accuracy investigation of Runge–Kutta methods”, Mat. Model., 22:5 (2010), 146–160; Math. Models Comput. Simul., 2:6 (2010), 800–811

Citation in format AMSBIB

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\by L.~M.~Skvortsov

\paper Model equations for accuracy investigation of Runge--Kutta methods

\jour Mat. Model.

\yr 2010

\vol 22

\issue 5

\pages 146--160

\mathnet{http://mi.mathnet.ru/mm2980}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2723855}

\transl

\jour Math. Models Comput. Simul.

\yr 2010

\vol 2

\issue 6

\pages 800--811

\crossref{https://doi.org/10.1134/S2070048210060165}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84929073186}

Linking options:

https://www.mathnet.ru/eng/mm2980

https://www.mathnet.ru/eng/mm/v22/i5/p146

This publication is cited in the following 8 articles:

L. M. Skvortsov, “Generalizations of the Stage Order of Runge–Kutta Methods”, Comput. Math. and Math. Phys., 64:12 (2024), 2796
L. M. Skvortsov, “Third- and fourth-order ESDIRK methods for stiff and differential-algebraic problems”, Comput. Math. Math. Phys., 46:5 (2022), 766–783
L. M. Skvortsov, “Implicit Runge–Kutta methods with explicit internal stages”, Comput. Math. Math. Phys., 58:3 (2018), 307–321
L. M. Skvortsov, “On implicit Runge–Kutta methods received as a result of inversion of explicit methods”, Math. Models Comput. Simul., 9:4 (2017), 498–510
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
L. M. Skvortsov, “Singly implicit diagonally extended Runge–Kutta methods of fourth order”, Comput. Math. Math. Phys., 54:5 (2014), 775–784
L. M. Skvortsov, “Runge–Kutta collocation methods for differential-algebraic equations of indices 2 and 3”, Comput. Math. Math. Phys., 52:10 (2012), 1373–1383
L. M. Skvortsov, “Explicit adaptive Runge–Kutta methods”, Math. Models Comput. Simul., 4:1 (2012), 82–91

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	596
Full-text PDF :	263
References:	67
First page:	21

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