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BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS
ISSN
2518-7929
2663-5011
Издатель
Karaganda Buketov University
4 результаты
Показано: 1 - 4 из 4
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Тип записи:Публикация, Numerical-analytical method for solving initial-boundary value problem for loaded parabolic equationAn initial-boundary value problem for a loaded parabolic equation in a rectangular domain was considered. By discretization with respect to a spatial variable, the problem under study is reduced to the initial problem for a system of loaded ordinary differential equations. Based on the previously obtained results of Dzhumabaev and Assanova, an estimate for the solution of the original initial-boundary value problem for a loaded parabolic equation was established. An auxiliary initial problem for a system of loaded ordinary differential equations is solved by the Dzhumabaev parameterization method. Conditions of the unique solvability of the considering problem are obtained and algorithms for finding a solution are constructed. The results are illustrated with a numerical example.Цитирования (OpenAlex) 6Цитирования (OpenCitations) 2 - 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, 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, Asymptotic convergence of the solution for singularly perturbed boundary value problem with boundary jumpsAsymptotic convergence of the solution for singularly perturbed boundary value problem with boundary jumpsThe article is devoted to study of boundary value problem with boundary jumps for third order linear integro-differential equation with a small parameter at the highest derivatives, provided that additional characteristic equation's roots have opposite signs.The modified unperturbed boundary value problem is constructed.The solution of modified unperturbed problem is obtained.Initial jumps' values of the integral term and solution are defined.An estimate difference of solution for singularly perturbed and modified unperturbed boundary value problems is obtained.The convergence of solution for singularly perturbed boundary value problem to solution of modified unperturbed boundary value problem is proved.Цитирования (OpenAlex) 6Цитирования (OpenCitations) 1