Қазақ ұлттық қыздар педагогикалық университеті / Казахский национальный женский педагогический университет
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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); Цитирования (OpenAlex) 3 - 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 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