Жарияланымдар / Публикации
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- Некоторые метрики заблокированы вашиминастройками согласия
Тип записи:Публикация, Numerical Solution to a Control Problem for Integro-Differential EquationsAbstract A control problem for an integro-differential equation is approximated by a problem with parameter for a loaded differential equation. A mutual relationship between the qualitative properties of the original and approximate problems is obtained, and estimates for the differences between their solutions are given. A numerical-approximate method for solving the control problem for the integro-differential equation is proposed, and the convergence, stability, and accuracy of the method are examined.Цитирования (OpenAlex) 65Цитирования (OpenCitations) 29 - Некоторые метрики заблокированы вашиминастройками согласия
Тип записи:Публикация, - 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, 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, 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, О ЧИСЛЕННОМ РЕШЕНИИ ЗАДАЧИ УПРАВЛЕНИЯ ДЛЯ ОБЫКНОВЕННЫХ ДИФФЕРЕНЦИ АЛЬНЫХ УРАВНЕНИЙ С МНОГОТОЧЕЧНЫМ УСЛОВИЕМ(2022-12-30); ; А.Б. КасымоваВ настоящей работе исследуется линейная краевая задача с параметром для обыкновенного дифференциального уравнения с многоточечным условием. На основе метода параметризации Джумабаева и численных методов разработан численный метод решения линейной краевой задачи с параметром для обыкновенного дифференциального уравнения с многоточечным условием и предложены алгоритмы их реализации. Разбиением интервала и введением дополнительных параметров линейная краевая задача с параметром для обыкновенных дифференциальных уравнений с многоточечным условием сводится к эквивалентной краевой задаче с параметром. Эквивалентная краевая задача с параметрами состоит из задачи Коши для системы обыкновенных дифференциальных уравнений с параметрами, многоточечного условия и условия склеивания. Решение задачи Коши для системы обыкновенных дифференциальных уравнений с параметрами строится с помощью фундаментальной матрицы дифференциального уравнения. Подставляя значения в соответствующих точках построенного решения в многоточечное условие и условие склеивания, составляется система линейных алгебраических уравнений относительно параметров. Предложен численный метод решения рассматриваемой задачи, основанный на решении построенной системы линейных алгебраических уравнений относительно параметров и метода Булирша-Штёра для решения задачи Коши для системы обыкновенных дифференциальных уравнений на подинтервалах. - 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, A new computational approach for solving a boundary-value problem for DEPCAG(2023-03-17); ; In this paper, a new computational approach is presented to solve a boundary-value problem for a differential equation with piecewise constant argument of generalized type (DEPCAG). The presented technique is based on the Dzhumabaev parametrization method. A useful numerical algorithm is developed to obtain the numerical values from the problem. Numerical experiments are conducted to demonstrate the accuracy and efficiency.Цитирования (OpenAlex) 4Цитирования (OpenCitations) 2 - Некоторые метрики заблокированы вашиминастройками согласия
Тип записи:Публикация, NUMERICAL IMPLEMENTATION FOR SOLVING THE BOUNDARY VALUE PROBLEM FOR IMPULSIVE INTEGRO-DIFFERENTIAL EQUATIONS WITH PARAMETERIn this paper, a linear boundary value problem under impulse effects for the system of Fredholm integro-differential equations with a parameter is investigated. The purpose of this research is to provide a method for solving the studied problem numerically. The ideas of the Dzhumabaev parameterisation method, classical numerical methods of solving Cauchy problems and numerical integration techniques were used as a basis for achieving the goal. When applying the method of parameterisation by points of impulse effects, the interval on which the boundary value problem is considered is divided, additional parameters and new unknown functions are introduced. As a consequence, a problem with parameters equivalent to the original problem is obtained. According to the data of the matrices of the integral term of the equation, boundary conditions and impulse conditions, the SLAE with respect to the introduced parameters is compiled. And the unknown functions are found as solutions of the initial-special problem for the system of integro-differential equations. A numerical algorithm for finding a solution to the boundary value problem for impulse integro-differential equations with a parameter is constructed. Numerical methods for solving Cauchy problems for ODE and calculating definite integrals are used for numerical implementation of the constructed algorithm. Numerical calculations are verified on test problem.Цитирования (OpenAlex) 18Цитирования (OpenCitations) 16 - 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