Қазақ ұлттық қыздар педагогикалық университеті / Казахский национальный женский педагогический университет

Постоянный URI для этого сообществаhttps://cris.qyzpu.edu.kz/handle/123456789/1

Просмотр

Фильтры

2024 - 20253

Настройки

Тема: search.filters.subject.rectangular domain

Результаты поиска

Показано: 1 - 3 из 3
  • Загрузка...
    Изображение-миниатюра
    Некоторые метрики заблокированы вашими 
    настройками согласия
    Тип записи:Публикация,
    ON A BOUNDARY VALUE PROBLEM FOR HIGH-ORDER HYPERBOLIC EQUATION WITH IMPULSE DISCRETE MEMORY
    (2024-10-02)
    A. T. Assanova
    ;
    R. A. Bimenova
    ;
    B. B. Мinglibayeva
    ;
    A. P. Sabalakhova
    The investigation focuses on a boundary value problem for a high-order hyperbolic equation with impulse discrete memory in a rectangular domain. By introducing new functions, the problem is transformed into a set of boundary value problems for a first-order differential equation with impulse discrete memory, which depends on unknown functions and integral relations. D.S. Dzhumabaev's parametrization method is applied to this equivalent problem. The domain is divided according to the time variable, and functional parameters representing discrete memory values are introduced within the interior domains. As a result, the family of boundary value problems for the first-order differential equation with impulse discrete memory and unknown functions is converted into an equivalent family of integral-multipoint boundary value problems involving functional parameters and unknown functions. These equivalent problems include initial value problems for first-order differential equations related to the new functions. The solutions to the initial value problems are expressed using Volterra integral equations. By substituting these solutions into the boundary and impulse conditions, a system of linear functional equations concerning the functional parameters is derived. An algorithm is developed to solve the equivalent problem, and sufficient conditions for the unique solvability of the family of integral-multipoint boundary value problems with functional parameters and unknown functions are provided. Additionally, sufficient conditions for the unique solvability of the original boundary value problem for the high-order hyperbolic equation with impulse discrete memory are established based on the initial data.
  • Загрузка...
    Изображение-миниатюра
    Некоторые метрики заблокированы вашими 
    настройками согласия
    Тип записи:Публикация,
    Research of the Finite Difference Numerical Method Using Artificial Intelligence for Solving Problems of Incompressible Fluid Flow in a Rectangular Domain with Initial and Boundary Conditions
    (2025-01-01)
    Lyailya Tukenova
    ;
    Omirlan Auelbekov
    ;
    S. Sapakova
    ;
    Bayan Abduraimova
    ;
    Ж. Р. Уалиев
    This study explores the enhancement of the finite difference method using artificial intelligence (AI) to model incompressible fluid flow within a rectangular domain.Accurate and efficient modeling of incompressible flows is crucial in hydrodynamics and aerodynamics, where traditional numerical methods like finite difference often face limitations in accuracy and computational speed, especially for complex problems with varied initial and boundary conditions.By integrating AI techniques such as neural networks and machine learning, this approach enables adaptive parameter selection, optimizing the calculation process, improving accuracy, and reducing computational demands.The combined finite difference and AI approach demonstrated significantly reduced computational complexity and improved accuracy, as verified across multiple test cases with different boundary conditions.Results indicate that AI-enhanced numerical methods improve the efficiency and reliability of solutions for complex hydrodynamic problems, offering faster, more precise modeling of fluid flow behaviors.The study highlights the potential of AI to enhance classical numerical methods, enabling the development of more accurate fluid flow models even with limited computational resources.The novelty of this work lies in the specific integration of machine learning with the finite difference method, presenting an adaptive approach that extends beyond traditional techniques.This integration opens up new possibilities for handling complex fluid dynamics scenarios, expanding the applications of numerical methods in scientific and engineering calculations.
  • Загрузка...
    Изображение-миниатюра
    Некоторые метрики заблокированы вашими 
    настройками согласия
    Тип записи:Публикация,
    Numerical-analytical method for solving initial-boundary value problem for loaded parabolic equation
    (Karaganda Buketov University, 2025-03-28)
    A. T. Assanova
    ;
    Zh. М. Каdirbayeva
    ;
    Saule Kuanysh
    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.
    Цитирования (OpenAlex) 6Цитирования (OpenCitations) 2