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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2021, Volume 62, Issue 6, Pages 20–26
DOI: https://doi.org/10.15372/PMTF20210603 (Mi pmtf67) 		 
Discrete method for solving a three-point boundary-value problem for a third-order equation

A. F. Voevodin, O. A. Frolovskaya

Lavrentyev Institute of Hydrodynamics of Siberian Branch of the Russian Academy of Sciences, 630090, Novosibirsk, Russia
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DOI: https://doi.org/10.15372/PMTF20210603
Abstract: Coupled equations are used to develop a method for solving boundary-value problems for second- and third-order equations. With the use of the factorization method, a three-point boundary-value problem for a third-order equation is reduced to a system of first- and second-order equations. In order to solve the second-order equation, a discrete problem is constructed, which is then used to solve the main problem. This method is peculiar because discrete (difference) boundary-value problems are constructed without using approximations of differential operators. The method is generalized to solve higher-order equations.
Keywords: boundary-value problem, coupled equation, difference scheme.
Received: 28.08.2020
Revised: 14.10.2020
Accepted: 30.11.2020
English version:
Journal of Applied Mechanics and Technical Physics, 2021, Volume 62, Issue 6, Pages 906–911
DOI: https://doi.org/10.1134/S0021894421060031
Bibliographic databases:
Document Type: Article
UDC: 519.624.3
Language: Russian
Citation: A. F. Voevodin, O. A. Frolovskaya, “Discrete method for solving a three-point boundary-value problem for a third-order equation”, Prikl. Mekh. Tekh. Fiz., 62:6 (2021), 20–26; J. Appl. Mech. Tech. Phys., 62:6 (2021), 906–911
Citation in format AMSBIB
\Bibitem{VoeFro21}
\by A.~F.~Voevodin, O.~A.~Frolovskaya
\paper Discrete method for solving a three-point boundary-value problem for a third-order equation
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2021
\vol 62
\issue 6
\pages 20--26
\mathnet{http://mi.mathnet.ru/pmtf67}
\crossref{https://doi.org/10.15372/PMTF20210603}
\elib{https://elibrary.ru/item.asp?id=47402199}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2021
\vol 62
\issue 6
\pages 906--911
\crossref{https://doi.org/10.1134/S0021894421060031}
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