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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2025 - 20262

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Автор: search.filters.author.Narkesh B. IskakovaТема: search.filters.subject.approximate solutions

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    Тип записи:Публикация,
    Numerical implementation of solving a boundary value problem including both delay and parameter
    (Springer Science+Business Media, 2025-06-01)
    Zh. М. Каdirbayeva
    ;
    Narkesh B. Iskakova
    ;
    E. А. Bakirova
    Abstract In this paper, a new technique, namely the Dzhumabaev parameterization method, is presented and applied to linear boundary value problem with parameter for delay differential equation to find an efficient algorithm for their approximate solutions. Effectiveness of this algorithm is tested by examples of second-order delay differential equations and linear boundary value problem with parameter for delay differential equations. Obtained results reveal that proposed algorithm of the Dzhumabaev parameterization method is highly efficient and straightforward to execute.
    Цитирования (OpenAlex) 3Цитирования (OpenCitations) 2
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    ON A BOUNDARY VALUE PROBLEM FOR A LOADED FRACTIONAL DIFFERENTIAL EQUATION
    (2026-09-25)
    Narkesh B. Iskakova
    ;
    E. А. Bakirova
    ;
    K. I. Usmanov
    ;
    N.T. Orumbayeva
    The paper investigates a two-point boundary value problem for a loaded differential e quation with a Caputo fractional derivative. The Dzhumabaev parametrization method is applied to study the problem. Within this approach, the initial interval is divided into a finite n umber of s ubintervals, a nd additional parameters and new functions are introduced, which makes it possible to reduce the original boundary value problem to an equivalent multipoint boundary value problem with unknown parameters. The equivalence of the original and transformed problems is established. Based on the obtained integral representations, a system of algebraic equations with respect to the introduced parameters is constructed. Sufficient conditions for the existence and uniqueness of a solution are established and related to the invertibility of the corresponding matrix. An algorithm based on the method of successive approximations is developed to determine the unknown parameters and functions. A numerical example demonstrating the application of the proposed algorithm and confirming its e ffectiveness is presented. The ob tained results de monstrate the efficiency of the pa rametrization me thod for in vestigating bo undary va lue pr oblems for lo aded fractionalorder differential e quations and c onstructing t heir a pproximate solutions.