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Matem. Mod., 2002, Volume 14, Number 2, Pages 3–17 (Mi mm653)  

This article is cited in 25 scientific papers (total in 25 papers)

Diagonally implicit Runge–Kutta FSAL methods for stiff and differential-algebraic systems

L. M. Skvortsov

N. E. Bauman Moscow State Technical University

Abstract: Implicit Runge-Kutta methods are considered which first stage coincides with the last stage of previous step. The methods of order 3, 4, 5 are proposed. Advantage of these methods in comparison with singly diagonally implicit Runge-Kutta methods is shown.

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Received: 29.11.2000

Citation: L. M. Skvortsov, “Diagonally implicit Runge–Kutta FSAL methods for stiff and differential-algebraic systems”, Matem. Mod., 14:2 (2002), 3–17

Citation in format AMSBIB
\Bibitem{Skv02}
\by L.~M.~Skvortsov
\paper Diagonally implicit Runge--Kutta FSAL methods for stiff and differential-algebraic systems
\jour Matem. Mod.
\yr 2002
\vol 14
\issue 2
\pages 3--17
\mathnet{http://mi.mathnet.ru/mm653}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1919848}
\zmath{https://zbmath.org/?q=an:1029.65080}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. L. M. Skvortsov, “Accuracy of the Runge–Kutta methods for stiff problems”, Comput. Math. Math. Phys., 43:9 (2003), 1320–1330  mathnet  mathscinet  zmath
    2. B. V. Rogov, M. N. Mikhailovskaya, “Some aspects of compact difference scheme convergence”, Math. Models Comput. Simul., 1:1 (2009), 91–104  mathnet  crossref  mathscinet  zmath
    3. L. M. Skvortsov, “The interpolation properties of Runge–Kutta methods”, Math. Models Comput. Simul., 1:6 (2009), 695–703  mathnet  crossref  mathscinet  zmath
    4. 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
    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. N. G. Bandurin, N. A. Gureeva, “Software package for the numerical solution of systems of essentially nonlinear ordinary integro-differential-algebraic equations”, Math. Models Comput. Simul., 4:5 (2012), 455–463  mathnet  crossref  mathscinet  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. L. M. Skvortsov, O. S. Kozlov, “Efficient implementation of diagonally implicit Runge–Kutta methods”, Math. Models Comput. Simul., 6:4 (2014), 415–424  mathnet  crossref
    11. L. M. Skvortsov, “Singly implicit diagonally extended Runge–Kutta methods of fourth order”, Comput. Math. Math. Phys., 54:5 (2014), 775–784  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    12. G. Yu. Kulikov, “Embedded symmetric nested implicit Runge–Kutta methods of Gauss and Lobatto types for solving stiff ordinary differential equations and Hamiltonian systems”, Comput. Math. Math. Phys., 55:6 (2015), 983–1003  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    13. Chikitkin A.V., Rogov B.V., Aristova E.N., “High-order accurate bicompact schemes for solving the multidimensional inhomogeneous transport equation and their efficient parallel implementation”, Dokl. Math., 94:2 (2016), 517–522  crossref  mathscinet  zmath  isi  elib  scopus
    14. Bragin M.D., Rogov B.V., “On exact dimensional splitting for a multidimensional scalar quasilinear hyperbolic conservation law”, Dokl. Math., 94:1 (2016), 382–386  crossref  mathscinet  zmath  isi  elib  scopus
    15. 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
    16. 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
    17. Rogov B.V. Bragin M.D., “On Spectral-Like Resolution Properties of Fourth-Order Accurate Symmetric Bicompact Schemes”, Dokl. Math., 96:1 (2017), 339–343  crossref  mathscinet  zmath  isi  scopus
    18. Chikitkin A.V., Rogov B.V., “A Sixth-Order Bicompact Scheme With Spectral-Like Resolution For Hyperbolic Equations”, Dokl. Math., 96:2 (2017), 480–485  crossref  mathscinet  zmath  isi  scopus
    19. Bragin M.D., Rogov B.V., “Iterative Approximate Factorization For Difference Operators of High-Order Bicompact Schemes For Multidimensional Nonhomogeneous Hyperbolic Systems”, Dokl. Math., 95:2 (2017), 140–143  crossref  mathscinet  zmath  isi  scopus
    20. A. V. Chikitkin, B. V. Rogov, “Semeistvo simmetrichnykh bikompaktnykh skhem so svoistvom spektralnogo razresheniya dlya uravnenii giperbolicheskogo tipa”, Preprinty IPM im. M. V. Keldysha, 2018, 144, 28 pp.  mathnet  crossref  elib
    21. M. D. Bragin, B. V. Rogov, “Iterative approximate factorization of difference operators of high-order accurate bicompact schemes for multidimensional nonhomogeneous quasilinear hyperbolic systems”, Comput. Math. Math. Phys., 58:3 (2018), 295–306  mathnet  crossref  crossref  isi  elib
    22. A. V. Chikitkin, B. V. Rogov, “Dva varianta parallelnoi realizatsii vysokotochnykh bikompaktnykh skhem dlya mnogomernogo neodnorodnogo uravneniya perenosa”, Preprinty IPM im. M. V. Keldysha, 2018, 177, 24 pp.  mathnet  crossref  elib
    23. M. D. Bragin, B. V. Rogov, “Konservativnaya monotonizatsiya bikompaktnykh skhem”, Preprinty IPM im. M. V. Keldysha, 2019, 008, 26 pp.  mathnet  crossref  elib
    24. M. D. Bragin, B. V. Rogov, “Bikompaktnye skhemy dlya mnogomernykh uravnenii giperbolicheskogo tipa na dekartovykh setkakh s adaptatsiei k resheniyu”, Preprinty IPM im. M. V. Keldysha, 2019, 011, 27 pp.  mathnet  crossref  elib
    25. B. V. Rogov, A. V. Chikitkin, “O skhodimosti i tochnosti metoda iteriruemoi priblizhennoi faktorizatsii operatorov mnogomernykh vysokotochnykh bikompaktnykh skhem”, Matem. modelirovanie, 31:12 (2019), 119–144  mathnet  crossref  elib
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