NUMERICAL METHOD FOR SOLVING THE BOUNDARY VALUE PROBLEM FOR THE PARABOLIC EQUATION

ПАРАБОЛАЛЫҚ ТЕҢДЕУ ҮШІН ШЕТТІК ЕСЕПТІ ШЕШУДІҢ САНДЫҚ ӘДІСІ
ЧИСЛЕННЫЙ МЕТОД РЕШЕНИЯ КРАЕВОЙ ЗАДАЧИ ДЛЯ ПАРАБОЛИЧЕСКОГО УРАВНЕНИЯ
Iskakova N.B. Kadirbayeva Z.М. Bakirova E.А. Kuanysh S.K.
2024 Kazakh-British Technical University

Herald of the Kazakh British Technical UNiversity
2024 #21 Issue 3 165 - 175 pp.

A linear boundary value problem for a parabolic equation is considered in a closed domain. Based on the broken line method, the boundary value problem for a parabolic equation is replaced by a two-point boundary value problem for a system of linear ordinary differential equations by discretizing the unknown function with respect to the variable. The obtained two-point boundary value problem is investigated by the parameterization method of Professor Dzhumabaev. Based on this method, an algorithm for finding a numerical solution to the two-point boundary value problem for a system of linear ordinary differential equations is constructed. The constructed algorithm is realized by applying known numerical methods. The constructiveness and efficiency of the parameterization method also allows us to construct a numerical solution of the considered linear boundary value problem for the parabolic equation. One numerical example is given to verify and illustrate the proposed algorithm.

algorithm , boundary value problem , numerical solution , Parabolic equation , parameterization method

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Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
Kazakh National Womens Teacher Training University, Almaty, 050000, Kazakhstan
International Information Technology University, Almaty, 050000, Kazakhstan

Institute of Mathematics and Mathematical Modeling
Al-Farabi Kazakh National University
Kazakh National Womens Teacher Training University
International Information Technology University

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