Жарияланымдар / Публикации
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Тип записи:Публикация, Method for solving the periodic problem for an impulsive system of hyperbolic integro-differential equationsThe periodic problem for a system of integro-differential equations of hyperbolic type with impulse effects is considered. This problem is reduced to an equivalent problem, consisting of a family of periodic boundary value problems for system of ordinary differential equations with parameter and impulse effects and integral relations by method of introducing additional functions. Sufficient conditions for existence of unique solution to the family of periodic boundary value problem with the impulse effects for system of the ordinary differential equations are received by parametrization method. Conditions for the unique solvability of periodic problem for system of integro - differential equations of hyperbolic type with impulse effects are established in the term of initial data.Цитирования (OpenAlex) 2Цитирования (OpenCitations) 2 - Некоторые метрики заблокированы вашиминастройками согласия
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, Numerical solution of a control problem for ordinary differential equations with multipoint integral condition(Al-Farabi Kazakh National University, 2019-12-20); ; A linear boundary value problem with a parameter for ordinary differential equations with multipoint integral conditionis investigated.The method of parameterization is used for solving the considered problem. The linear boundary value problem with a parameter for ordinary differential equations with multipoint integral condition by introducing additional parameters at the partition points is reduced to equivalent boundary value problem with parameters. The equivalent boundary value problem with parameters consists of the Cauchy problem for the system of ordinary differential equations with parameters, multipoint integral condition and continuity conditions. The solution of the Cauchy problem for the system of ordinary differential equations with parameters is constructed using the fundamental matrix of differential equation. The system of linear algebraic equations with respect to the parameters are composed by substituting the values of the corresponding points in the built solutions to the multipoint integral condition and the continuity condition. Numerical method for finding solution of the problem is suggested, which based on the solving the constructed system and Runge-Kutta method of the 4-th order for solving Cauchy problem on the subintervals.Цитирования (OpenAlex) 6Цитирования (OpenCitations) 2 - 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, О РАЗРЕШИМОСТИ ЛИНЕЙНОЙ МНОГОТОЧЕЧНОЙ КРАЕВОЙ ЗАДАЧИ ДЛЯ СИСТЕМ ОБЫКНОВЕННЫХ ДИФФЕРЕНЦИАЛЬНЫХ УРАВНЕНИЙ(2021-03-21)A linear multipoint boundary value problem for the system of ordinary differential equations is considered. The method of parameterization is used for solving the considering problem. The linear multipoint boundary value problem for the system of ordinary differential equations by introducing additional parameters at the ends and at points of partition of the interval is reduced to an equivalent boundary value problem with parameters. The article is illustrated by an example for finding the solution of the linear three-point boundary value problem for the system of ordinary differential equations. - 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, A novel numerical implementation for solving problem for loaded DEPCAG(Al-Farabi Kazakh National University, 2023-01-10); Цитирования (OpenAlex) 8Цитирования (OpenCitations) 7