Жарияланымдар / Публикации
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- Некоторые метрики заблокированы вашиминастройками согласия
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, Recovery problem for a singularly perturbed differential equation with an initial jumpThe article investigates the asymptotic behavior of the solution to reconstructing the boundary conditions and the right-hand side for second-order differential equations with a small parameter at the highest derivative, which have an initial jump. Asymptotic estimates of the solution of the reconstruction problem are obtained for singularly perturbed second-order equations with an initial jump. The rules for the restoration of boundary conditions and the right parts of the original and degenerate problems are established. The asymptotic estimates of the solution of the perturbed problem are determined as well as the difference between the solution of the degenerate problem and the solution of the perturbed problem. A theorem on the existence, uniqueness, and representation of a solution to the reconstruction problem from the position of singularly perturbed equations is proved. The results obtained open up possibilities for the further development of the theory of singularly perturbed boundary value problems for ordinary differential equations.Цитирования (OpenAlex) 4Цитирования (OpenCitations) 1 - 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, Convergence, stability, and error analysis of the method of lines for solving loaded parabolic equations(American Institute of Mathematical Sciences, 2025-01-01); Цитирования (OpenAlex) 3 - 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.