Numerical-analytical method for solving initial-boundary value problem for loaded parabolic equation
Assanova A.T. Kadirbayeva Zh.M. Kuanysh S.K.
2025E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2025#117Issue 134 - 45 pp.
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.
initial-boundary value problem , loaded parabolic equations , numerical solution , parameterization method , polygonal method , solvability conditions
Text of the article Перейти на текст статьи
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Kazakh National Women’s Teacher Training University, Almaty, Kazakhstan
Al-Farabi Kazakh National University, Almaty, Kazakhstan
Institute of Mathematics and Mathematical Modeling
Kazakh National Women’s Teacher Training University
Al-Farabi Kazakh National University
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026