Қазақ ұлттық қыздар педагогикалық университеті / Казахский национальный женский педагогический университет
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- 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 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 - Некоторые метрики заблокированы вашиминастройками согласия
Тип записи:Публикация, NUMERICAL SOLUTION OF A BOUNDARY VALUE PROBLEM WITH A PARAMETER FOR IMPULSIVE LOADED DIFFERENTIAL EQUATIONS(2024-07-01); ; The boundary value problem depending on the parameter for the system of impulsive loaded differential equations is considered. Algorithms of numerical realization of the Dzhumabaev parameterization method are developed for numerical solving of the studied boundary value problem depending on the parameter. Algorithms of numerical realization of the Dzhumabaev parameterization method are based on the solving of Cauchy problems for the system of ordinary differential equations. As a result of application of the proposed method, finding a solution to the boundary value problem depending on the parameter for impulsive loaded differential equations leads to finding a solution to the system of algebraic equations. This system of algebraic equations consists of a boundary condition and equalities with respect to the conditions at the impulsive points. Numerical results showing the high efficiency of the numerical implementation of the Dzhumabaev parameterization method are given. The result demonstrate that there is congruence between the numerical and the exact results to a high order of accuracy. - 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 implementation of solving a boundary value problem including both delay and parameter(Springer Science+Business Media, 2025-06-01); Цитирования (OpenAlex) 3Цитирования (OpenCitations) 2 - 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 - Некоторые метрики заблокированы вашиминастройками согласия
Тип записи:Публикация, Application of the Parameterization Method to Nonlinear Boundary Value Problem With a Nonfixed Moment of Impulsive ActionABSTRACT This paper investigates a nonlinear boundary value problem for a system of linear differential equations with a nonfixed moment of impulsive action. To address this problem, we apply the Dzhumabaev parameterization method, which is adapted to account for the nonlinearity of the boundary conditions and the presence of an unknown impulsive moment. These features required modifications of the classical schemes of the method, leading to the development of new algorithms that incorporate the non‐fixed impulsive action. The main contribution of this work is the extension of the applicability of the parameterization method and the derivation of solvability conditions for the problem under consideration. To illustrate the theoretical results, an example is presented.Цитирования (OpenAlex) 1Цитирования (OpenCitations) 1