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Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 9, Pages 1497–1514 (Mi zvmmf10089)  

This article is cited in 11 scientific papers (total in 11 papers)

A numerical method for solving one nonlocal boundary value problem for a third-order hyperbolic equation

M. Kh. Beshtokov

Kabardino-Balkar State University, ul. Chernyshevskogo 173, Nalchik, 360004, Russia

Abstract: A nonlocal boundary value problem for a third-order hyperbolic equation with variable coefficients is considered in the one- and multidimensional cases. A priori estimates for the nonlocal problem are obtained in the differential and difference formulations. The estimates imply the stability of the solution with respect to the initial data and the right-hand side on a layer and the convergence of the difference solution to the solution of the differential problem.

Key words: boundary value problems, nonlocal condition, a priori estimate, difference scheme, stability and convergence of difference schemes, third-order hyperbolic equation, pseudo-parabolic equation.

DOI: https://doi.org/10.7868/S0044466914090051

Full text: PDF file (893 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2014, 54:9, 1441–1458

Bibliographic databases:

UDC: 519.633
Received: 12.04.2012
Revised: 22.03.2013

Citation: M. Kh. Beshtokov, “A numerical method for solving one nonlocal boundary value problem for a third-order hyperbolic equation”, Zh. Vychisl. Mat. Mat. Fiz., 54:9 (2014), 1497–1514; Comput. Math. Math. Phys., 54:9 (2014), 1441–1458

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. T. K. Yuldashev, “Nelineinoe integro-differentsialnoe uravnenie psevdoparabolicheskogo tipa s nelokalnym integralnym usloviem”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2016, no. 1(32), 11–23  mathnet  crossref
    2. T. K. Yuldashev, “Smeshannoe differentsialnoe uravnenie tipa Bussineska”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2016, no. 2(33), 13–26  mathnet  crossref
    3. M. Kh. Beshtokov, “Difference method for solving a nonlocal boundary value problem for a degenerating third-order pseudo-parabolic equation with variable coefficients”, Comput. Math. Math. Phys., 56:10 (2016), 1763–1777  mathnet  crossref  crossref  isi  elib
    4. T. K. Yuldashev, “Nonlocal problem for a mixed type differential equation in rectangular domain”, Uch. zapiski EGU, ser. Fizika i Matematika, 2016, no. 3, 70–78  mathnet
    5. M. Kh. Beshtokov, “On the numerical solution of a nonlocal boundary value problem for a degenerating pseudoparabolic equation”, Differ. Equ., 52:10 (2016), 1341–1354  crossref  mathscinet  zmath  isi  elib  scopus
    6. T. K. Yuldashev, “Mixed problem for pseudoparabolic integro-differential equation with degenerate kernel”, Differ. Equ., 53:1 (2017), 99–108  crossref  mathscinet  zmath  isi  elib  elib  scopus
    7. T. K. Yuldashev, “Nonlocal mixed-value problem for a Boussinesq-type integrodifferential equation with degenerate kernel”, Ukr. Math. J., 68:8 (2017), 1278–1296  crossref  mathscinet  isi  scopus
    8. T. K. Yuldashev, “Nelokalnaya kraevaya zadacha dlya neodnorodnogo psevdoparabolicheskogo integro-differentsialnogo uravneniya s vyrozhdennym yadrom”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2017, no. 1(38), 42–54  mathnet  crossref
    9. M. Kh. Beshtokov, V. Z. Kanchukoev, F. A. Erzhibova, “O skhodimosti raznostnykh skhem, approksimiruyuschikh kraevuyu zadachu dlya psevdoparabolicheskogo uravneniya s vyrozhdeniem”, Vladikavk. matem. zhurn., 19:4 (2017), 13–26  mathnet
    10. M. Kh. Beshtokov, “Differential and difference boundary value problem for loaded third-order pseudo-parabolic differential equations and difference methods for their numerical solution”, Comput. Math. Math. Phys., 57:12 (2017), 1973–1993  mathnet  crossref  crossref  isi  elib
    11. M. Kh. Beshtokov, “Boundary value problems for degenerating and nondegenerating Sobolev-type equations with a nonlocal source in differential and difference forms”, Differ. Equ., 54:2 (2018), 250–267  crossref  mathscinet  zmath  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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