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Lobachevskii Journal of Mathematics
ISSN
1818-9962
1995-0802
Издатель
Pleiades Publishing
3 результаты
Показано: 1 - 3 из 3
- Некоторые метрики заблокированы вашиминастройками согласия
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