Қазақ ұлттық қыздар педагогикалық университеті / Казахский национальный женский педагогический университет

Постоянный URI для этого сообществаhttps://cris.qyzpu.kz/handle/123456789/1

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2024 - 20263

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Автор: search.filters.author.Narkesh B. IskakovaТема: search.filters.subject.Cauchy problem

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    ON THE UNIQUE SOLVABILITY OF A BOUNDARY VALUE PROBLEM FOR DIFFERENTIAL EQUATIONS WITH PARAMETER
    (2024-03-25)
    E. А. Bakirova
    ;
    Narkesh B. Iskakova
    ;
    Svetlana Temesheva
    ;
    Zh. М. Каdirbayeva
    A linear boundary value problem for a differential equation with a parameter is investigated on a finite interval by the parameterization method. The studied boundary value problem with parameter is reduced to an equivalent multipoint boundary value problem with parameters by splitting the interval, introducing additional parameters at the points of splitting and new functions. The obtained equivalent boundary value problem contains Cauchy problems for ordinary differential equations with respect to new functions. By substituting the solution representation of the Cauchy problem into the boundary conditions and continuity conditions of the solution, a system of linear algebraic equations with respect to the introduced parameters is compiled. An algorithm for finding a solution to the boundary value problem with parameters is constructed. The formulation of the theorem on sufficient conditions of unique solvability of the boundary value problem with parameters is given. Sufficient conditions of its unique solvability are obtained in terms of the data of the original boundary value problem. An example showing the fulfillment of the conditions of the theorem is given.
    Цитирования (OpenAlex) 1Цитирования (OpenCitations) 1
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    An Algorithm for Solving Boundary Value Problems for Delay Differential Equations with Loadings
    (Pleiades Publishing, 2024-10-01)
    Narkesh B. Iskakova
    ;
    E. А. Bakirova
    ;
    Б.С. Ханжарова
    ;
    Zh. М. Каdirbayeva
    Abstract In this paper, we propose an efficient numerical algorithm for solving linear two-point boundary value problem for delay differential equations with loadings. The Dzhumabaev parametrization method is applied to construct the numerical solutions. The application of the this method leads the considering problem to a system of algebraic equations and Cauchy problems for differential equation without delay argument that are easy to solve. Several illustrative examples are given to demonstrate the effectiveness of the proposed algorithm.
    Цитирования (OpenAlex) 8Цитирования (OpenCitations) 4
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    A new numerical technique for solving a multipoint problem with parameter for impulsive integro-differential equations
    (Springer Science+Business Media, 2026-07-15)
    E. А. Bakirova
    ;
    Zh. М. Каdirbayeva
    ;
    Narkesh B. Iskakova
    Abstract In this paper, we offer a new numerical technique for solving the linear multipoint problem with parameter for impulsive integro-differential equations. The proposed technique is based on the Dzhumabaev’s parameterization method, one of the ideas of which is to solve a system of linear algebraic equations. The coefficients and right-hand sides of the system are determined by solving Cauchy problems for ordinary differential equations. The given numerical examples showed the efficiency and accuracy of the introduced algorithm.