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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 5, Pages 828–836 (Mi zvmmf11077)  

This article is cited in 1 scientific paper (total in 1 paper)

Numerical solution of linear differential equations with nonlocal nonlinear conditions

K. R. Aida-zade

Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku, AZ1141 Azerbaijan

Abstract: The numerical solution of systems of linear ordinary differential equations with nonlocal nonlinear conditions depending on the values of the desired function at intermediate points is investigated. Conditions for the existence of a solution to the problem under consideration are given. For the numerical solution, an approach is proposed that reduces the problem to two auxiliary linear systems of differential equations with linear conditions and to a single nonlinear algebraic system with a dimension depending only on the number of given intermediate points. The proposed approach is illustrated by solving two problems. The auxiliary problems are solved analytically in one of them and numerically in the other.

Key words: linear differential equations, nonlocal nonlinear conditions, fundamental solution matrix, Cauchy formula, algebraic equation.

DOI: https://doi.org/10.31857/S0044466920030035


English version:
Computational Mathematics and Mathematical Physics, 2020, 60:5, 808–816

Bibliographic databases:

UDC: 517.927.6
Received: 14.06.2019
Revised: 14.06.2019
Accepted:14.01.2020

Citation: K. R. Aida-zade, “Numerical solution of linear differential equations with nonlocal nonlinear conditions”, Zh. Vychisl. Mat. Mat. Fiz., 60:5 (2020), 828–836; Comput. Math. Math. Phys., 60:5 (2020), 808–816

Citation in format AMSBIB
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\paper Numerical solution of linear differential equations with nonlocal nonlinear conditions
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2020
\vol 60
\issue 5
\pages 828--836
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\crossref{https://doi.org/10.31857/S0044466920030035}
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\transl
\jour Comput. Math. Math. Phys.
\yr 2020
\vol 60
\issue 5
\pages 808--816
\crossref{https://doi.org/10.1134/S0965542520030033}
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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. K. R. Aida-zade, E. R. Ashrafova, “Upravlenie vozdeistviyami v pravykh chastyakh bolshoi sistemy ODU blochnoi struktury i optimizatsiya istochnikov v nerazdelennykh kraevykh usloviyakh”, Sib. zhurn. vychisl. matem., 24:3 (2021), 229–251  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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