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 - Некоторые метрики заблокированы вашиминастройками согласия
Тип записи:Публикация, Analysis of Semi-periodic Problem for Integro-differential Equations of Parabolic TypeAbstract In this paper, we investigate a semi-periodic boundary-value problem for parabolic integro-differential equations. To solving this problem, we employ spatial discretization via the method of lines, which transforms the continuous formulation into a discrete one. The resulting system is then treated by means of Dzhumabaev’s parameterization technique, reducing it to an equivalent Cauchy-type problem for a system of Fredholm integro-differential equations with periodic and continuity conditions imposed at the partition points. The construction of the solution relies on the fundamental matrix. Theoretical results are established to clarify the relationship between the original integro-differential formulation and its discretized counterpart. A numerical algorithm is further developed, which involves solving the auxiliary system, applying the classical fourth-order Runge-Kutta method to the Cauchy problems on subintervals, and employing Simpson’s rule to approximate definite integrals. Numerical experiments on test problems demonstrate both the accuracy and efficiency of the proposed approach. - Некоторые метрики заблокированы вашиминастройками согласия
Тип записи:Публикация, Stability and convergence analysis of Fredholm-type parabolic integro-differential equations(Elsevier BV, 2026-08-28); ; ; Saule Kuanysh