Қазақ ұлттық қыздар педагогикалық университеті / Казахский национальный женский педагогический университет
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Тип записи:Публикация, NUMERICAL METHOD FOR SOLVING THE BOUNDARY VALUE PROBLEM FOR THE PARABOLIC EQUATION(2024-10-01); ; Saule KuanyshA 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 u(t,x) with respect to the variable x. 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. - Некоторые метрики заблокированы вашиминастройками согласия
Тип записи:Публикация, METHOD OF LINES FOR A LOADED PARABOLIC EQUATION(Al-Farabi Kazakh National University, 2025-03-25); In a closed domain, a two-point boundary value problem for loaded parabolic equations is considered. The method of lines with respect to the variable x is used to solve this problem. As a result of this approach, a discretized problem is formulated. The discretized problem is reduced to a two-point boundary value problem for loaded differential equations (LDE). The solution of the resulting boundary value problem is performed using the parameterization method developed by professor Dzhumabaev. The study demonstrates the relationship between the boundary value problem for the loaded parabolic equation and the related discretized problem.Цитирования (OpenAlex) 7Цитирования (OpenCitations) 3 - Некоторые метрики заблокированы вашиминастройками согласия
Тип записи:Публикация, Analysis of Nonlocal Problem for Loaded Parabolic Equation via Numerical MethodAbstract This paper investigates a nonlocal problem for a loaded parabolic equation defined on a closed domain. By applying spatial discretization, the original problem is transformed into a two-point boundary value problem for a system of loaded ordinary differential equations. To address this problem, the Dzhumabaev parameterization method is utilized. Based on this approach, a numerical algorithm is developed to solve the original problem. The effectiveness of the proposed method is demonstrated through two computational examples. The obtained numerical results are compared with the exact solutions to validate the accuracy of the algorithm.Цитирования (OpenAlex) 2