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Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 4, Pages 520–529 (Mi zvmmf10715)  

This article is cited in 7 scientific papers (total in 7 papers)

Numerical solution of systems of loaded ordinary differential equations with multipoint conditions

A. T. Assanovaa, A. E. Imanchiyevb, Zh. M. Kadirbaevaa

a Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science of the Republic of Kazakhstan, Almaty, Kazakhstan
b Aktobe Regional State University, Aktobe, Kazakhstan

Abstract: A system of loaded ordinary differential equations with multipoint conditions is considered. The problem under study is reduced to an equivalent boundary value problem for a system of ordinary differential equations with parameters. A system of linear algebraic equations for the parameters is constructed using the matrices of the loaded terms and the multipoint condition. The conditions for the unique solvability and well-posedness of the original problem are established in terms of the matrix made up of the coefficients of the system of linear algebraic equations. The coefficients and the righthand side of the constructed system are determined by solving Cauchy problems for linear ordinary differential equations. The solutions of the system are found in terms of the values of the desired function at the initial points of subintervals. The parametrization method is numerically implemented using the fourth-order accurate Runge–Kutta method as applied to the Cauchy problems for ordinary differential equations. The performance of the constructed numerical algorithms is illustrated by examples.

Key words: system of loaded differential equations, multipoint condition, algorithm for finding approximate solutions.

Funding Agency Grant Number
Ministry of Education and Science of the Republic of Kazakhstan 0822/ГФ4


DOI: https://doi.org/10.7868/S0044466918040038

References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2018, 58:4, 508–516

Bibliographic databases:

UDC: 519.62
Received: 28.03.2017
Revised: 29.05.2017

Citation: A. T. Assanova, A. E. Imanchiyev, Zh. M. Kadirbaeva, “Numerical solution of systems of loaded ordinary differential equations with multipoint conditions”, Zh. Vychisl. Mat. Mat. Fiz., 58:4 (2018), 520–529; Comput. Math. Math. Phys., 58:4 (2018), 508–516

Citation in format AMSBIB
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\paper Numerical solution of systems of loaded ordinary differential equations with multipoint conditions
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2018
\vol 58
\issue 4
\pages 520--529
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\crossref{https://doi.org/10.7868/S0044466918040038}
\elib{https://elibrary.ru/item.asp?id=32825774}
\transl
\jour Comput. Math. Math. Phys.
\yr 2018
\vol 58
\issue 4
\pages 508--516
\crossref{https://doi.org/10.1134/S096554251804005X}
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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. Assanova A.T., Boichuk A.A., Tokmurzin Z.S., “On the Initial-Boundary Value Problem For System of the Partial Differential Equations of Fourth Order”, News Natl. Acad. Sci. Rep. Kazakhstan-Ser. Phys.-Math., 1:323 (2019), 14–21  crossref  isi
    2. A. T. Assanova, A. E. Imanchiyev, Zh. M. Kadirbayeva, “Solvability of nonlocal problems for systems of Sobolev-type differential equations with a multipoint condition”, Russian Math. (Iz. VUZ), 63:12 (2019), 1–12  mathnet  crossref  crossref  isi
    3. A. T. Asanova, A. Zholamankyzy, “O semeistve dvukhtochechnykh kraevykh zadach dlya nagruzhennykh differentsialnykh uravnenii”, Izv. vuzov. Matem., 2021, no. 9, 13–24  mathnet  crossref
    4. A. T. Assanova, A. Zholamankyzy, “Problem with data on the characteristics for a loaded system of hyperbolic equations”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 31:3 (2021), 353–364  mathnet  crossref
    5. K. U. Khubiev, “Ob odnom analoge zadachi Trikomi dlya «tochechno» nagruzhennogo uravneniya giperbolo-parabolicheskogo tipa”, Vestnik KRAUNTs. Fiz.-mat. nauki, 36:3 (2021), 29–39  mathnet  crossref
    6. A. T. Asanova, Sh. T. Shekerbekova, “O nachalno-kraevoi zadache dlya sistemy nagruzhennykh differentsialnykh uravnenii chetvertogo poryadka”, Differentsialnye uravneniya i matematicheskaya fizika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 198, VINITI RAN, M., 2021, 3–21  mathnet  crossref
    7. K. U. Khubiev, “Zadacha Bitsadze—Samarskogo dlya nagruzhennogo giperbolo-parabolicheskogo uravneniya c vyrozhdeniem poryadka v oblasti ego giperbolichnosti”, Differentsialnye uravneniya i matematicheskaya fizika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 198, VINITI RAN, M., 2021, 123–132  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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