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Lobachevskii Journal of Mathematics
ISSN
1818-9962
1995-0802
Издатель
Pleiades Publishing
7 результаты
Показано: 1 - 7 из 7
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Тип записи:Публикация, On the Unique Solvability of a Family of Boundary Value Problems for Integro-Differential Equations of Mixed TypeAbstract The family of boundary value problems for a system of integro-differential equations of mixed type is considered. First, considered problem is reduced to the family of boundary value problems for the Fredholm integro-differential equations with an unknown function and the integral relation. Further, based on the introduction of an additional parameter as a value of the solution at the beginning line of the domain, the problem is reduced to an equivalent problem containing the family of Cauchy problems for the system of Fredholm integro-differential equations with a parameter and the unknown function, and the hybrid system of functional and integral equations for the parameter and the unknown function, respectively. Conditions for the unique solvability of the considered problem are obtained in the terms of the solvability to family of Cauchy problems and the hybrid system.Цитирования (OpenAlex) 6Цитирования (OpenCitations) 5 - 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, Solution to an Identification Parameter Problem for System of Nonlinear Differential EquationsAbstract The inverse problem with identification parameter for system of ordinary differential equations is considered. Definition of the isolated solution for the inverse problem with identification parameter to nonlinear system of ordinary differential equations is introduced. For finding of the isolated solution to problem is used the parametrization method. The method consists in partitioning of the considered interval, introducing of parameters and reducing the original problem to the equivalent multi-point identification parameter problem. The algorithms for finding an approximate solution to the equivalent problem are offered. Each step of the algorithm consists of two stages: a) solving of the nonlinear system of equations with respect to the parameters, composed by the initial data of the problem, and b) solving the Cauchy problems on corresponding intervals at the founded parameters values. The conditions for convergence of the algorithms that ensure the solvability of the inverse problem with identification parameter are established. The necessary and sufficient conditions for the existence of the isolated solution to the inverse problem with identification parameter are obtained in the terms of the right-hand side of the system of differential equations and the boundary conditions.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, 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, 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, Analysis of Semi-periodic Problem for Integro-differential Equations of Parabolic TypeAbstract In this paper, we investigate a semi-periodic boundary-value problem for parabolic integro-differential equations. To solving this problem, we employ spatial discretization via the method of lines, which transforms the continuous formulation into a discrete one. The resulting system is then treated by means of Dzhumabaev’s parameterization technique, reducing it to an equivalent Cauchy-type problem for a system of Fredholm integro-differential equations with periodic and continuity conditions imposed at the partition points. The construction of the solution relies on the fundamental matrix. Theoretical results are established to clarify the relationship between the original integro-differential formulation and its discretized counterpart. A numerical algorithm is further developed, which involves solving the auxiliary system, applying the classical fourth-order Runge-Kutta method to the Cauchy problems on subintervals, and employing Simpson’s rule to approximate definite integrals. Numerical experiments on test problems demonstrate both the accuracy and efficiency of the proposed approach.