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Matematicheskoe modelirovanie, 2011, Volume 23, Number 7, Pages 73–87 (Mi mm3132)  
This article is cited in 5 scientific papers (total in 5 papers)

Explicit adaptive Runge–Kutta methods

L. M. Skvortsov

Bauman Moscow State Technical University
Full-text PDF (365 kB) Citations (5)
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Abstract: Adjusting the parameters of the integration formula to the problem under solution allows us to increase considerably efficiency of explicit Runge–Kutta methods when solving stiff problems. Construction of such adaptive methods is considered. Results of the solution of test problems in comparison with known methods are presented.
Keywords: explicit Runge–Kutta methods, stiff problems, nonstiff problems.
Received: 07.12.2010
English version:
Mathematical Models and Computer Simulations, 2012, Volume 4, Issue 1, Pages 82–91
DOI: https://doi.org/10.1134/S2070048212010127
Bibliographic databases:
Document Type: Article
UDC: 519.622
Language: Russian
Citation: L. M. Skvortsov, “Explicit adaptive Runge–Kutta methods”, Mat. Model., 23:7 (2011), 73–87; Math. Models Comput. Simul., 4:1 (2012), 82–91
Citation in format AMSBIB
\Bibitem{Skv11}
\by L.~M.~Skvortsov
\paper Explicit adaptive Runge--Kutta methods
\jour Mat. Model.
\yr 2011
\vol 23
\issue 7
\pages 73--87
\mathnet{http://mi.mathnet.ru/mm3132}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2895744}
\transl
\jour Math. Models Comput. Simul.
\yr 2012
\vol 4
\issue 1
\pages 82--91
\crossref{https://doi.org/10.1134/S2070048212010127}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84928989867}
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  • https://www.mathnet.ru/eng/mm3132
  • https://www.mathnet.ru/eng/mm/v23/i7/p73
    • This publication is cited in the following 5 articles:
    1. Hong-Yan Zhang, Fei Liu, Yu Zhou, Man Liang, “Even Order Explicit Symplectic Geometric Algorithms for Solving Quaternions in Guidance Navigation and Control via Diagonal Padé Approximation and Cayley Transform”, IEEE Access, 12 (2024), 105906  crossref
    2. E. B. Kuznetsov, S. S. Leonov, E. D. Tsapko, “Estimating the domain of absolute stability of a numerical scheme based on the method of solution continuation with respect to a parameter for solving stiff initial value problems”, Comput. Math. Math. Phys., 63:4 (2023), 528–541  mathnet  mathnet  crossref  crossref
    3. L. M. Skvortsov, “Construction and analysis of explicit adaptive one-step methods for solving stiff problems”, Comput. Math. Math. Phys., 60:7 (2020), 1078–1091  mathnet  crossref  crossref  isi  elib
    4. Douglas Mossman, Hongying Peng, “Using Dual Beta Distributions to Create 'Proper' ROC Curves Based on Rating Category Data”, SSRN Journal, 2014  crossref
    5. L. M. Skvortsov, “Efficient implementation of second order implicit Runge–Kutta methods”, Math. Models Comput. Simul., 5:6 (2013), 565–574  mathnet  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математическое моделирование
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    Abstract page:854
    Full-text PDF :666
    References:72
    First page:11
     
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