Қазақ ұлттық қыздар педагогикалық университеті / Казахский национальный женский педагогический университет

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Автор: search.filters.author.Saule KuanyshЕсть файлы: Да

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    Тип записи:Публикация,
    Convergence, stability, and error analysis of the method of lines for solving loaded parabolic equations
    (American Institute of Mathematical Sciences, 2025-01-01)
    A. T. Assanova
    ;
    Zhenhai Liu
    ;
    Saule Kuanysh
    ;
    Zh. М. Каdirbayeva
    This paper studies the method of lines for solving loaded parabolic equations and provides a theoretical analysis of its convergence, stability, and error estimates. The spatial discretization reduces the original equation to a system of loaded ordinary differential equations solved by the Dzhumabaev parameterization method. Sufficient conditions for the existence and uniqueness of the solution are established, and it is proved that the method achieves second-order accuracy in space and stable convergence. A numerical example confirms the efficiency and reliability of the proposed approach.
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    Numerical-analytical method for solving initial-boundary value problem for loaded parabolic equation
    (Karaganda Buketov University, 2025-03-28)
    A. T. Assanova
    ;
    Zh. М. Каdirbayeva
    ;
    Saule Kuanysh
    An initial-boundary value problem for a loaded parabolic equation in a rectangular domain was considered. By discretization with respect to a spatial variable, the problem under study is reduced to the initial problem for a system of loaded ordinary differential equations. Based on the previously obtained results of Dzhumabaev and Assanova, an estimate for the solution of the original initial-boundary value problem for a loaded parabolic equation was established. An auxiliary initial problem for a system of loaded ordinary differential equations is solved by the Dzhumabaev parameterization method. Conditions of the unique solvability of the considering problem are obtained and algorithms for finding a solution are constructed. The results are illustrated with a numerical example.
    Цитирования (OpenAlex) 6Цитирования (OpenCitations) 2