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Zh. Vychisl. Mat. Mat. Fiz., 2003, Volume 43, Number 9, Pages 1374–1384 (Mi zvmmf964)  

This article is cited in 15 scientific papers (total in 15 papers)

Accuracy of the Runge–Kutta methods for stiff problems

L. M. Skvortsov

N. E. Bauman Moscow State Technical University

Full text: PDF file (1517 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2003, 43:9, 1320–1330

Bibliographic databases:
UDC: 519.622
MSC: Primary 65L06; Secondary 34A34, 65L70, 65L05
Received: 29.04.2002

Citation: L. M. Skvortsov, “Accuracy of the Runge–Kutta methods for stiff problems”, Zh. Vychisl. Mat. Mat. Fiz., 43:9 (2003), 1374–1384; Comput. Math. Math. Phys., 43:9 (2003), 1320–1330

Citation in format AMSBIB
\Bibitem{Skv03}
\by L.~M.~Skvortsov
\paper Accuracy of the Runge--Kutta methods for stiff problems
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2003
\vol 43
\issue 9
\pages 1374--1384
\mathnet{http://mi.mathnet.ru/zvmmf964}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2014988}
\zmath{https://zbmath.org/?q=an:1077.65081}
\transl
\jour Comput. Math. Math. Phys.
\yr 2003
\vol 43
\issue 9
\pages 1320--1330


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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, “Explicit Runge–Kutta methods for moderately stiff problems”, Comput. Math. Math. Phys., 45:11 (2005), 1939–1951  mathnet  mathscinet  zmath
    2. L. M. Skvortsov, “Explicit multistep method for the numerical solution of stiff differential equations”, Comput. Math. Math. Phys., 47:6 (2007), 915–923  mathnet  crossref
    3. L. M. Skvortsov, “An efficient scheme for the implementation of implicit Runge–Kutta methods”, Comput. Math. Math. Phys., 48:11 (2008), 2007–2017  mathnet  crossref  mathscinet  isi
    4. L. M. Skvortsov, “Explicit two-step Runge–Kutta methods”, Math. Models Comput. Simul., 2:2 (2010), 222–231  mathnet  crossref  mathscinet  zmath
    5. L. M. Skvortsov, “A simple technique for constructing two-step Runge–Kutta methods”, Comput. Math. Math. Phys., 49:11 (2009), 1837–1846  mathnet  crossref  isi
    6. L. M. Skvortsov, “Model equations for accuracy investigation of Runge–Kutta methods”, Math. Models Comput. Simul., 2:6 (2010), 800–811  mathnet  crossref  mathscinet
    7. L. M. Skvortsov, “Diagonally implicit Runge-Kutta methods for differential-algebraic equations of indices 2 and 3”, Comput. Math. Math. Phys., 50:6 (2010), 993–1005  mathnet  crossref  mathscinet  adsnasa  isi
    8. L. M. Skvortsov, “Explicit stabilized Runge–Kutta methods”, Comput. Math. Math. Phys., 51:7 (2011), 1153–1166  mathnet  crossref  mathscinet  isi  elib
    9. 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  mathnet  crossref  mathscinet  zmath
    10. P. D. Shirkov, “Stability of ROW methods for non autonomous systems of ordinary differential equations”, Math. Models Comput. Simul., 4:6 (2012), 587–596  mathnet  crossref  mathscinet  elib
    11. Leonov G.A., Burova I.G., Aleksandrov K.D., “Visualization of Four Limit Cycles of Two-Dimensional Quadratic Systems in the Parameter Space”, Differ. Equ., 49:13 (2013), 1675–1703  crossref  mathscinet  zmath  isi  elib  scopus
    12. L. M. Skvortsov, “A fifth order implicit method for the numerical solution of differential-algebraic equations”, Comput. Math. Math. Phys., 55:6 (2015), 962–968  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    13. 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  mathnet  crossref  elib
    14. 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
    15. 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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