On solvability of boundary value problem for a nonlinear Fredholm integro-differential equation

Фредгольм сызықты емес интегралдық-дифференциалдық теңдеуi үшiн шеттiк есептiң шешiлiмдiлiгi туралы
О разрешимости краевой задачи для нелинейного интегро-дифференциального уравнения Фредгольма
Assanova A.T. Zhumatov S.S. Mynbayeva S.T. Karakenova S.G.
2022 E.A. Buketov Karaganda University Publish house

Bulletin of the Karaganda University. Mathematics Series
2022 #105 Issue 1 25 - 34 pp.

The paper proposes a constructive method to solve a nonlinear boundary value problem for a Fredholm integro-differential equation. Using D.S. Dzhumabaev parametrization method, the problem under consideration is transformed into an equivalent boundary value problem for a system of nonlinear integro-differential equations with parameters on the subintervals. When applying the parametrization method to a nonlinear Fredholm integro-differential equation, the intermediate problem is a special Cauchy problem for a system of nonlinear integro-differential equations with parameters. By substitution the solution to the special Cauchy problem with parameters into the boundary condition and the continuity conditions of the solution to the original problem at the interior partition points, we construct a system of nonlinear algebraic equations in parameters. It is proved that the solvability of this system provides the existence of a solution to the original boundary value problem. The iterative methods are used to solve both the constructed system of algebraic equations in parameters and the special Cauchy problem. An algorithm for solving boundary value problem under consideration is provided.

algorithm , boundary value problem , Dzhumabaev parametrization method , isolated solution , iterative process , nonlinear Fredholm integro-differential equation , special Cauchy problem

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Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Al-Farabi Kazakh National University, Almaty, Kazakhstan
K.Zhubanov Aktobe Regional University, Aktobe, Kazakhstan

Institute of Mathematics and Mathematical Modeling
Al-Farabi Kazakh National University
K.Zhubanov Aktobe Regional University

10 лет помогаем публиковать статьи Международный издатель

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