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 Sib. Zh. Ind. Mat., 2012, Volume 15, Number 3, Pages 3–15 (Mi sjim734)

Solution of differential equations with nonseparated multipoint and integral conditions

V. M. Abdullaev

Institute of Cybernetics NAS of Azerbaijan, Baku, Azerbaijan

Abstract: We propose a numerical method for solving systems of linear nonautonomous ordinary differential equations with nonseparated multipoint and integral conditions. The method is based on the operation of the convolution of the integral conditions into local ones, which allows us to reduce the solution of the original problem to the solution of a Cauchy problem for ordinary differential equations and for a system of algebraic linear equations. We prove the stability of the computational schemes. Many numerical experiments on specially constructed test problems with the use of the formulas and schemes for numerical solution are proposed in the article. The experimental results showed a sufficiently high efficiency of this approach.

Keywords: system of ordinary differential equations, nonseparated conditions, integral conditions, nonlocal multipoint conditions, operation of successive shift.

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UDC: 519.621.2

Citation: V. M. Abdullaev, “Solution of differential equations with nonseparated multipoint and integral conditions”, Sib. Zh. Ind. Mat., 15:3 (2012), 3–15

Citation in format AMSBIB
\Bibitem{Abd12} \by V.~M.~Abdullaev \paper Solution of differential equations with nonseparated multipoint and integral conditions \jour Sib. Zh. Ind. Mat. \yr 2012 \vol 15 \issue 3 \pages 3--15 \mathnet{http://mi.mathnet.ru/sjim734} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3098804} 

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This publication is cited in the following articles:
1. 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”, Num. Anal. Appl., 7:1 (2014), 1–14
2. K. R. Aida-zade, Y. R. Ashrafova, “Solving a system of differential equations of block structure with unseparated boundary conditions”, J. Appl. Industr. Math., 9:1 (2015), 1–10
3. V. M. Abdullaev, K. R. Aida-zade, “Numerical method of solution to loaded nonlocal boundary value problems for ordinary differential equations”, Comput. Math. Math. Phys., 54:7 (2014), 1096–1109
4. V. R. Barseghyan, T. V. Barseghyan, “On an approach to the problems of control of dynamic systems with nonseparated multipoint intermediate conditions”, Autom. Remote Control, 76:4 (2015), 549–559
5. K. R. Aida-zade, E. R. Ashrafova, “Raschet perekhodnykh rezhimov dvizheniya zhidkosti v truboprovodnykh setyakh”, Sib. zhurn. industr. matem., 18:2 (2015), 12–23
6. 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
7. V. R. Barsegyan, “Zadacha upravleniya dlya odnoi sistemy lineinykh nagruzhennykh differentsialnykh uravnenii s nerazdelennymi mnogotochechnymi promezhutochnymi usloviyami”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 21 (2017), 19–32
8. 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
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