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
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.
linear differential equations, nonlocal nonlinear conditions, fundamental solution matrix, Cauchy formula, algebraic equation.
Computational Mathematics and Mathematical Physics, 2020, 60:5, 808–816
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
\paper Numerical solution of linear differential equations with nonlocal nonlinear conditions
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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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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