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Sib. Zh. Vychisl. Mat., 2014, Volume 17, Number 1, Pages 1–16 (Mi sjvm527)  

This article is cited in 13 scientific papers (total in 13 papers)

On the numerical solution to loaded systems of ordinary differential equations with non-separated multipoint and integral conditions

K. R. Aida-zadea, V. M. Abdullaevb

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

Abstract: We propose a numerical method of solving systems of linear non-autonomous ordinary loaded differential equations with non-separated multipoint and integral conditions. This method is based on the operation of convolution of integral conditions to local conditions. This approach allows reducing the solution to the original problem to solving the Cauchy problem with respect to a system of ordinary differential equations and to linear algebraic equations. Numerous computational experiments on several test problems with application of the formulas and schemes of the numerical solution have been carried out. The results of the experiments have shown a sufficiently high efficiency of the approach described.

Key words: ordinary loaded differential equations system, non-separated conditions, integral conditions, non-local multipoint conditions, sequential shift operation.

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English version:
Numerical Analysis and Applications, 2014, 7:1, 1–14

Bibliographic databases:

UDC: 519.621.2
Received: 18.01.2013
Revised: 29.03.2013

Citation: K. R. Aida-zade, V. M. Abdullaev, “On the numerical solution to loaded systems of ordinary differential equations with non-separated multipoint and integral conditions”, Sib. Zh. Vychisl. Mat., 17:1 (2014), 1–16; Num. Anal. Appl., 7:1 (2014), 1–14

Citation in format AMSBIB
\by K.~R.~Aida-zade, V.~M.~Abdullaev
\paper On the numerical solution to loaded systems of ordinary differential equations with non-separated multipoint and integral conditions
\jour Sib. Zh. Vychisl. Mat.
\yr 2014
\vol 17
\issue 1
\pages 1--16
\jour Num. Anal. Appl.
\yr 2014
\vol 7
\issue 1
\pages 1--14

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    This publication is cited in the following articles:
    1. K. R. Aida-zade, Y. R. Ashrafova, “Calculation of a state of the system of discrete linear processes connected by nonseparated boundary conditions”, J. Appl. Industr. Math., 10:4 (2016), 457–467  mathnet  crossref  crossref  mathscinet  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. 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
    4. Z. Khankishiyev, “On solution of a nonlocal problem with dynamic boundary conditions for a loaded linear parabolic equation by straight-line methods”, Bull. Comput. Appl. Math., 5:1 (2017), 77–98  mathscinet  isi
    5. 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
    6. A. T. Assanova, Zh. M. Kadirbayeva, “On the numerical algorithms of parametrization method for solving a two-point boundary-value problem for impulsive systems of loaded differential equations”, Comput. Appl. Math., 37:4 (2018), 4966–4976  crossref  mathscinet  zmath  isi  scopus
    7. D. S. Dzhumabaev, “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  zmath  isi  scopus
    8. 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
    9. V. M. Abdullayev, “Numerical solution to optimal control problems with multipoint and integral conditions”, Proc. Inst. Math. Mech., 44:2 (2018), 171–186  mathscinet  zmath  isi
    10. K. R. Aida-zade, V. M. Abdullayev, “Optimization of the placements of observation points in one problem of control of heating process”, IFAC-PapersOnLine, 51:30 (2018), 245–250  crossref  isi  scopus
    11. I. N. Parasidis, “Extension method for a class of loaded differential equations with nonlocal integral boundary conditions”, Bull. Karaganda Univ-Math., 96:4 (2019), 58–68  crossref  isi
    12. Bakirova E.A., Iskakova N.B., Assanova A.T., “Numerical Method For the Solution of Linear Boundary-Value Problems For Integrodifferential Equations Based on Spline Approximations”, Ukr. Math. J., 71:9 (2020), 1341–1358  crossref  mathscinet  isi  scopus
    13. 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
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