Қазақ ұлттық қыздар педагогикалық университеті / Казахский национальный женский педагогический университет
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Тип записи:Публикация, On one algorithm for finding a solution to a two-point boundary value problem for loaded differential equations with impulse effectOn one algorithm for finding a solution to a two-point boundary value problem for loaded differential equations with impulse effect A linear two-point boundary value problem for a system of loaded differential equations with impulse effect is investigated.The parameterization method is used to solve the problem.The essence of parameterization method is that segment, where the loaded differential equation is considered, is divided into parts by loading points, and the initial problem is reduced to the boundary value problem with a parameter.The solution to boundary value problem with parameter is defined as a limit of systems sequence, consisting of the pairs of parameter and function.Parameters are defined by a system of linear algebraic equations.System of linear algebraic equations is determined by the matrices of boundary conditions, the system of loaded differential equations, and the conditions of impulse effect.An algorithm for finding the solution to linear two-point boundary value problem for the systems of loaded differential equations with impulse effect is offered.The convergence conditions of the algorithm providing the existence and uniqueness of solution to the considered problem are established.Sufficient conditions for unique solvability of the problem in the terms of initial data are received.Цитирования (OpenAlex) 13Цитирования (OpenCitations) 7 - Некоторые метрики заблокированы вашиминастройками согласия
Тип записи:Публикация, AN ALGORITHM FOR SOLVING A BOUNDARY VALUE PROBLEM FOR ESSENTIALLY LOADED DIFFERENTIAL EQUATIONS(2021-04-15); ; ; A linear boundary value problem for essentially loaded differential equations is considered. Using the properties of essentially loaded differential we reduce the considering problem to a two-point boundary value problem for loaded differential equations. This problem is investigated by parameterization method. We offer algorithm for solving to boundary value problem for the system of loaded differential equations. This algorithm includes of the numerical solving of the Cauchy problems for system of the ordinary differential equations and solving of the linear system of algebraic equations. For numerical solving of the Cauchy problem we apply the Runge–Kutta method of 4th order. The proposed numerical implementation is illustrated by example.Цитирования (OpenAlex) 1 - Некоторые метрики заблокированы вашиминастройками согласия
Тип записи:Публикация, A Computational Method for Solving a Boundary-Value Problem for Differential Equations with Piecewise Constant Argument of Generalized TypeAbstract In this article, a two-point boundary-value problem for a differential equation with piecewise constant argument of generalized type is solved. We develop a numerical algorithm that is based on the parametrization method proposed by Dzhumabaev. The proposed algorithm is expanded to find a numerical solution to the boundary-value problem for differential equations with piecewise constant argument of generalized type. The results are illustrated by numerical example.Цитирования (OpenAlex) 9Цитирования (OpenCitations) 6 - Некоторые метрики заблокированы вашиминастройками согласия
Тип записи:Публикация, A novel numerical implementation for solving problem for loaded DEPCAG(Al-Farabi Kazakh National University, 2023-01-10); Цитирования (OpenAlex) 8Цитирования (OpenCitations) 7 - Некоторые метрики заблокированы вашиминастройками согласия
Тип записи:Публикация, Two-Point Boundary Value Problem for Volterra–Fredholm Integro-Differential Equations and Its Numerical AnalysisAbstract A two-point boundary value problem for Volterra–Fredholm integro-differential equations is considered. To solve this problem, Dzhumabaev parametrization method is used. Conditions for the existence and uniqueness of two-point boundary value problem for Volterra–Fredholm integro-differential equations are established. An algorithm for finding solution of this problem is proposed. Then, numerical approach for analysis of two-point boundary value problem for Volterra–Fredholm integro-differential equations is offered. Results are illustrated by numerical example.Цитирования (OpenAlex) 7Цитирования (OpenCitations) 7 - Некоторые метрики заблокированы вашиминастройками согласия
Тип записи:Публикация, An Algorithm for Solving Boundary Value Problems for Delay Differential Equations with Loadings(Pleiades Publishing, 2024-10-01); ; Abstract In this paper, we propose an efficient numerical algorithm for solving linear two-point boundary value problem for delay differential equations with loadings. The Dzhumabaev parametrization method is applied to construct the numerical solutions. The application of the this method leads the considering problem to a system of algebraic equations and Cauchy problems for differential equation without delay argument that are easy to solve. Several illustrative examples are given to demonstrate the effectiveness of the proposed algorithm.Цитирования (OpenAlex) 8Цитирования (OpenCitations) 4 - Некоторые метрики заблокированы вашиминастройками согласия
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, ON THE APPROXIMATION OF A BOUNDARY VALUE PROBLEM FOR DELAY INTEGRO-DIFFERENTIAL EQUATIONS(2025-07-06); - 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