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Analysis of Semi-periodic Problem for Integro-differential Equations of Parabolic Type
Автор(ы)
Дата публикации
1 декабря 2025 г.
Тип
journal article
Издатель
Pleiades Publishing
Том
46
Выпуск
12
Первая страница
6441
Последняя страница
6454
ISSN
1818-9962
Аннотация
Abstract 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.
Области науки (FoS)