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Zh. Vychisl. Mat. Mat. Fiz., 2004, Volume 44, Number 8, Pages 1388–1409 (Mi zvmmf793)  

This article is cited in 14 scientific papers (total in 14 papers)

On multistep methods of the interpolation type with an automated checking of the global error

G. Yu. Kulikovab, S. K. Shindinab

a School of Computational and Applied Mathematics, University of the Witmatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa
b Ulyanovsk State University, Faculty of Mathematics and Mechanics

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English version:
Computational Mathematics and Mathematical Physics, 2004, 44:8, 1314–1333

Bibliographic databases:
UDC: 519.622.2
MSC: Primary 65L06; Secondary 65L07, 34A30, 65L70
Received: 19.11.2002

Citation: G. Yu. Kulikov, S. K. Shindin, “On multistep methods of the interpolation type with an automated checking of the global error”, Zh. Vychisl. Mat. Mat. Fiz., 44:8 (2004), 1388–1409; Comput. Math. Math. Phys., 44:8 (2004), 1314–1333

Citation in format AMSBIB
\by G.~Yu.~Kulikov, S.~K.~Shindin
\paper On multistep methods of the interpolation type with an automated checking of the global error
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2004
\vol 44
\issue 8
\pages 1388--1409
\jour Comput. Math. Math. Phys.
\yr 2004
\vol 44
\issue 8
\pages 1314--1333

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    This publication is cited in the following articles:
    1. Kulikov G.Y., Shindin S.K., “Global error estimation and extrapolated multistep methods for index 1 differential-algebraic systems”, BIT. Numerical Mathematics, 45:3 (2005), 517–542  crossref  mathscinet  zmath  isi  elib  scopus
    2. Kulikov G.Y., Shindin S.K., “On stable integration of stiff ordinary differential equations with global error control”, Computational science—ICCS 2005. Part I, Lecture Notes in Comput. Sci., 3514, Springer, Berlin, 2005, 42–49  crossref  mathscinet  zmath  isi
    3. Kulikov G.Yu., Shindin S.K., “One-leg variable-coefficient formulas for ordinary differential equations and local-global step size control”, Numer. Algorithms, 43:1 (2006), 99–121  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. G. Yu. Kulikov, E. Y. Khrustaleva, “Automatic step size and order control in implicit one-step extrapolation methods”, Comput. Math. Math. Phys., 48:9 (2008), 1545–1569  mathnet  crossref  mathscinet  isi
    5. Kulikov G.Yu., Shindin S.K., “Local and global error estimation in Nordsieck methods”, Russian J. Numer. Anal. Math. Modelling, 23:6 (2008), 567–595  crossref  mathscinet  zmath  isi  elib  scopus
    6. Orel B., “Accumulation of global error in Lie group methods for linear ordinary differential equations”, Electron. Trans. Numer. Anal., 37 (2010), 252–262  mathscinet  zmath  isi
    7. Kulikov G.Yu., Weiner R., “Variable-stepsize interpolating explicit parallel peer methods with inherent global error control”, SIAM J. Sci. Comput., 32:4 (2010), 1695–1723  crossref  mathscinet  zmath  isi  scopus
    8. Kulikov G.Yu., Weiner R., “Global error control in implicit parallel peer methods”, Russian J. Numer. Anal. Math. Modelling, 25:2 (2010), 131–146  crossref  mathscinet  zmath  isi  elib  scopus
    9. Kulikov G.Yu., Weiner R., “Global error estimation and control in linearly-implicit parallel two-step peer W-methods”, J Comput Appl Math, 236:6 (2011), 1226–1239  crossref  mathscinet  zmath  isi  elib  scopus
    10. G. Yu. Kulikov, “Solving the order reduction phenomenon in variable step size quasi-consistent Nordsieck methods”, Comput. Math. Math. Phys., 52:11 (2012), 1547–1564  mathnet  crossref  mathscinet  isi  elib  elib
    11. Weiner R., Kulikov G.Yu., Podhaisky H., “Variable-Stepsize Doubly Quasi-Consistent Parallel Explicit Peer Methods with Global Error Control”, Appl. Numer. Math., 62:10, SI (2012), 1591–1603  crossref  mathscinet  zmath  isi  scopus
    12. Kulikov G.Yu., “Global Error Control in Adaptive Nordsieck Methods”, SIAM J. Sci. Comput., 34:2 (2012), A839–A860  crossref  mathscinet  zmath  isi  scopus
    13. Kulikov G.Yu., “Adaptive Nordsieck Formulas with Advanced Global Error Control Mechanisms”, Russ. J. Numer. Anal. Math. Model, 28:4 (2013), 321–352  crossref  mathscinet  zmath  isi  elib
    14. R. Weiner, G. Yu. Kulikov, “Efficient error control in numerical integration of ordinary differential equations and optimal interpolating variable-stepsize peer methods”, Comput. Math. Math. Phys., 54:4 (2014), 604–619  mathnet  crossref  crossref  mathscinet  isi  elib  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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