Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya
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Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya, 2019, Volume 15, Issue 4, Pages 502–517
DOI: https://doi.org/10.21638/11701/spbu10.2019.407
(Mi vspui424)
 

This article is cited in 2 scientific papers (total in 2 papers)

Applied mathematics

Two-parametric family of sixth order numerical methods for solving systems of ordinary differential equations

I. V. Olemskoy, N. A. Kovrizhnykh, O. S. Firyulina

St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
Full-text PDF (416 kB) Citations (2)
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Abstract: The paper is devoted to the construction of economical explicit sixth-order numerical method for solving structurally partitioned systems of ordinary differential equations. The general form of the method, which algorithmically uses the properties of the system structure, is presented. Conditions of order six, which the parameters of the method must satisfy, are derived. The simplifying conditions are found, which reduces the large nonlinear system of order conditions to a solvable smaller system. A solution with two free parameters is obtained. Economic explicit sixth-order schemes for systems of ordinary differential equations are presented. Numerical tests to compare to known explicit sixth-order one-step methods are performed.
Keywords: order, the order conditions, simplifying conditions.
Received: November 2, 2019
Accepted: November 7, 2019
Document Type: Article
UDC: 519.62/.642
MSC: 65L06
Language: Russian
Citation: I. V. Olemskoy, N. A. Kovrizhnykh, O. S. Firyulina, “Two-parametric family of sixth order numerical methods for solving systems of ordinary differential equations”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 15:4 (2019), 502–517
Citation in format AMSBIB
\Bibitem{OleKovFir19}
\by I.~V.~Olemskoy, N.~A.~Kovrizhnykh, O.~S.~Firyulina
\paper Two-parametric family of sixth order numerical methods for solving systems of ordinary differential equations
\jour Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr.
\yr 2019
\vol 15
\issue 4
\pages 502--517
\mathnet{http://mi.mathnet.ru/vspui424}
\crossref{https://doi.org/10.21638/11701/spbu10.2019.407}
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Вестник Санкт-Петербургского университета. Серия 10. Прикладная математика. Информатика. Процессы управления
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    Abstract page:102
    Full-text PDF :22
    References:18
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