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Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 7, Pages 1096–1109 (Mi zvmmf10061)  

This article is cited in 18 scientific papers (total in 18 papers)

Numerical method of solution to loaded nonlocal boundary value problems for ordinary differential equations

V. M. Abdullaevab, K. R. Aida-zadeab

a Institute of Cybernetics, Academy of Sciences of Azerbaijan, ul. B. Vagabzade 9, Baku, AZ1141, Azerbaijan
b Azerbaijan State Oil Academy, pr. Azadlyg 20, Baku, AZ1010, Azerbaijan

Abstract: A numerical method is suggested for solving systems of nonautonomous loaded linear ordinary differential equations with nonseparated multipoint and integral conditions. The method is based on the convolution of integral conditions into local ones. As a result, the original problem is reduced to an initial value (Cauchy) problem for systems of ordinary differential equations and linear algebraic equations. The approach proposed is used in combination with the linearization method to solve systems of loaded nonlinear ordinary differential equations with nonlocal conditions. An example of a loaded parabolic equation with nonlocal initial and boundary conditions is used to show that the approach can be applied to partial differential equations. Numerous numerical experiments on test problems were performed with the use of the numerical formulas and schemes proposed.

Key words: loaded systems of ordinary differential equations, nonseparated conditions, integral conditions, nonlocal multipoint conditions, numerical method.

DOI: https://doi.org/10.7868/S0044466914070023

Full text: PDF file (859 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2014, 54:7, 1096–1109

Bibliographic databases:

UDC: 519.624
MSC: 34A30, 65L10
Received: 01.08.2013

Citation: V. M. Abdullaev, K. R. Aida-zade, “Numerical method of solution to loaded nonlocal boundary value problems for ordinary differential equations”, Zh. Vychisl. Mat. Mat. Fiz., 54:7 (2014), 1096–1109; Comput. Math. Math. Phys., 54:7 (2014), 1096–1109

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Aida-zade K.R., Abdullayev V.M., “Solution to a class of inverse problems for a system of loaded ordinary differential equations with integral conditions”, J. Inverse Ill-Posed Probl., 24:5 (2016), 543–558  crossref  mathscinet  zmath  isi  elib
    2. E. A. Bakirova, N. B. Iskakova, “An approach to the choice of the initial approximation of the solution of nonlinear boundary value problem for loaded differential equations”, Bull. Karaganda Univ-Math., 84:4 (2016), 8–17  isi
    3. V. M. Abdullayev, K. R. Aida-zade, “Optimization of loading places and load response functions for stationary systems”, Comput. Math. Math. Phys., 57:4 (2017), 634–644  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. K. R. Aida-zade, V. M. Abdullayev, “Optimizing placement of the control points at synthesis of the heating process control”, Autom. Remote Control, 78:9 (2017), 1585–1599  mathnet  crossref  isi  elib
    5. D. S. Dzhumabaev, S. M. Temesheva, “Approximation of problem for finding the bounded solution to system of nonlinear loaded differential equations”, News Natl. Acad. Sci. Rep. Kazakhstan-Ser. Phys.-Math., 1:311 (2017), 13+  isi
    6. V. M. Abdullayev, “Identification of the functions of response to loading for stationary systems”, Cybern. Syst. Anal., 53:3 (2017), 417–425  crossref  mathscinet  zmath  isi  scopus
    7. K. R. Aida-zade, Y. R. Ashrafova, “Numerical leak detection in a pipeline network of complex structure with unsteady flow”, Comput. Math. Math. Phys., 57:12 (2017), 1919–1934  mathnet  crossref  crossref  isi  elib
    8. A. T. Asanova, Zh. M. Kadirbaeva, E. A. Bakirova, “On the unique solvability of a nonlocal boundary-value problem for systems of loaded hyperbolic equations with impulsive actions”, Ukr. Math. J., 69:8 (2018), 1175–1195  crossref  mathscinet  isi  scopus
    9. D. Dzhumabaev, “Computational methods of solving the boundary value problems for the loaded differential and Fredholm integro-differential equations”, Math. Meth. Appl. Sci., 41:4 (2018), 1439–1462  crossref  mathscinet  zmath  isi  scopus
    10. D. S. Dzhuraabaev, “Well-posedness of nonlocal boundary value problem for a system of loaded hyperbolic equations and an algorithm for finding its solution”, J. Math. Anal. Appl., 461:1 (2018), 817–836  crossref  mathscinet  isi  scopus
    11. K. R. Aida-zade, V. A. Hashimov, “Optimization of measurement points positioning in a border control synthesis problem for the process of heating a rod”, Autom. Remote Control, 79:9 (2018), 1643–1660  mathnet  crossref  isi  elib
    12. A. T. Assanova, A. E. Imanchiyev, Zh. M. Kadirbaeva, “Numerical solution of systems of loaded ordinary differential equations with multipoint conditions”, Comput. Math. Math. Phys., 58:4 (2018), 508–516  mathnet  crossref  crossref  isi  elib
    13. K. R. Aida-Zade, V. M. Abdullayev, “Numerical solution to optimal control problems for loaded dynamic systems with integral conditions”, Proceedings of the 6th International Conference on Control and Optimization With Industrial Applications, v. I, eds. A. Fikret, B. Tamer, Baku State Univ., Inst. Applied Mathematics, 2018, 107–109  isi
    14. I. N. Parasidis, E. Providas, “An exact solution method for a class of nonlinear loaded difference equations with multipoint boundary conditions”, J. Differ. Equ. Appl., 24:10 (2018), 1649–1663  crossref  mathscinet  zmath  isi  scopus
    15. K. Aida-Zade, V. Hashimov, “On one problem of synthesis of lumped controls on heating the plate”, Proceedings of the 6th International Conference on Control and Optimization With Industrial Applications, v. II, eds. A. Fikret, B. Tamer, Baku State Univ., Inst. Applied Mathematics, 2018, 41–43  isi
    16. V. M. Abdullaev, “Chislennoe reshenie kraevoi zadachi dlya nagruzhennogo parabolicheskogo uravneniya s nelokalnymi granichnymi usloviyami”, Vestnik KRAUNTs. Fiz.-mat. nauki, 32:3 (2020), 15–28  mathnet  crossref
    17. K. R. Aida-zade, V. M. Abdullayev, “Optimization of right-hand sides of nonlocal boundary conditions in a controlled dynamical system”, Autom. Remote Control, 82:3 (2021), 375–397  mathnet  crossref  crossref  isi  elib
    18. 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
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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