Қазақ ұлттық қыздар педагогикалық университеті / Казахский национальный женский педагогический университет
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- Некоторые метрики заблокированы вашиминастройками согласия
Тип записи:Публикация, MODIFICATION OF THE PARAMETRIZATION METHOD FOR SOLVING A BOUNDARY VALUE PROBLEM FOR LOADED DIFFERENTIAL EPCAG(Al-Farabi Kazakh National University, 2022-09-27); ; In this paper, modification of Dzhumabaev parameterization method is developed to a boundary value problem for systems of loaded differential equations with piecewise constant argument of generalized type (EPCAG). The method is based on reducing the considering problem to an equivalent multi-point boundary value problem for ordinary differential equations with parameters. An equivalent boundary value problem with parameters consists of the Cauchy problem for a system of ordinary differential equations with parameters, a two-point condition, a continuity condition, and additional conditions for a piecewise constant argument. The solution of the Cauchy problem for a system of ordinary differential equations with parameters is constructed using the fundamental matrix of the differential equation. A system of linear algebraic equations for the parameters is compiled using the values of the solution at the corresponding points and substituting them into the two-point condition, the continuity condition, and the conditions for the piecewise constant argument. A modification of Dzhumabaev parameterization method for solving the considering boundary value problem is proposed which is based on solving the constructed system and the 4th order Runge-Kutta method for solving the Cauchy problem on subintervals. The obtained results are verified by a numerical example. Numerical analysis showed high efficiency of the constructed modification of Dzhumabaev parameterization method.Цитирования (OpenAlex) 4Цитирования (OpenCitations) 2 - Некоторые метрики заблокированы вашиминастройками согласия
Тип записи:Публикация, Solving multi-point problem for Volterra-Fredholm integro-differential equations using Dzhumabaev parameterization methodAbstract In this study, a multipoint boundary value problem for Volterra-Fredholm integro-differential equations is considered. The addition of a new function converts the system of Volterra-Fredholm integro-differential equations to a system of Fredholm integro-differential equations. In contrast to the original problem, the dimension of a Fredholm integro-differential equation is determined by the number of matrices in the degenerate kernel of the Volterra integral. A numerical algorithm of Dzhumabaev parameterization method for addressing a multipoint boundary value problem for Volterra-Fredholm integro-differential equations is proposed. The main advantage of the proposed method is splitting the problem into auxiliary Cauchy problems for ordinary differential equations and a system of algebraic equations with respect to the parameters. The conditions for the unique solvability of the multipoint boundary value problem for Fredholm integro-differential equations are established. Finally, various numerical examples are provided to demonstrate the efficiency and correctness of the suggested technique.Цитирования (OpenAlex) 7Цитирования (OpenCitations) 3 - Некоторые метрики заблокированы вашиминастройками согласия
Тип записи:Публикация, ON THE UNIQUE SOLVABILITY OF A BOUNDARY VALUE PROBLEM FOR DIFFERENTIAL EQUATIONS WITH PARAMETER(2024-03-25); Цитирования (OpenAlex) 1Цитирования (OpenCitations) 1 - Некоторые метрики заблокированы вашиминастройками согласия
Тип записи:Публикация, SOLVABILITY OF A MULTIPOINT BOUNDARY VALUE PROBLEM FOR LOADED DIFFERENTIAL EQUATIONS WITH A PARAMETER(2025-09-27); S. AshirovThis article is devoted to the solvability questions of a multipoint boundary value problem for a system of loaded differential equations with a parameter. The investigation is carried out using the Dzhumabaev parameterization method. This allows us to reduce the solving of the original boundary value problem to the solving of a system of algebraic equations and Cauchy problems for ordinary differential equations. Modifications have been introduced into the parametrization method algorithms to reduce the influence of boundary conditions on the convergence of the algorithm. Following the specifics of the parametrization method, sufficient conditions for the existence and uniqueness of a solution to the multipoint boundary value problem for systems of loaded differential equations with a parameter have been established. These conditions also ensure the convergence of the modified algorithms. The research results provide a constructive tool for analyzing the behavior of various models described by boundary value problems for loaded differential equations with parameters. The presented example clearly demonstrates the feasibility and effectiveness of the proposed method. - Некоторые метрики заблокированы вашиминастройками согласия
Тип записи:Публикация, A new numerical technique for solving a multipoint problem with parameter for impulsive integro-differential equations(Springer Science+Business Media, 2026-07-15); ; Narkesh B. IskakovaAbstract In this paper, we offer a new numerical technique for solving the linear multipoint problem with parameter for impulsive integro-differential equations. The proposed technique is based on the Dzhumabaev’s parameterization method, one of the ideas of which is to solve a system of linear algebraic equations. The coefficients and right-hand sides of the system are determined by solving Cauchy problems for ordinary differential equations. The given numerical examples showed the efficiency and accuracy of the introduced algorithm. - Некоторые метрики заблокированы вашиминастройками согласия
Тип записи:Публикация, ON A BOUNDARY VALUE PROBLEM FOR A LOADED FRACTIONAL DIFFERENTIAL EQUATION(2026-09-25);