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Journal of Mathematics Mechanics and Computer Science
ISSN
1563-0277
2617-4871
Издатель
Al-Farabi Kazakh National University
2 результаты
Показано: 1 - 2 из 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, MODIFICATION OF THE PARAMETRIZATION METHOD FOR SOLVING A BOUNDARY VALUE PROBLEM FOR LOADED DIFFERENTIAL EPCAG(Al-Farabi Kazakh National University, 2022-09-27); ; In this paper, modification of Dzhumabaev parameterization method is developed to a boundary value problem for systems of loaded differential equations with piecewise constant argument of generalized type (EPCAG). The method is based on reducing the considering problem to an equivalent multi-point boundary value problem for ordinary differential equations with parameters. An equivalent boundary value problem with parameters consists of the Cauchy problem for a system of ordinary differential equations with parameters, a two-point condition, a continuity condition, and additional conditions for a piecewise constant argument. The solution of the Cauchy problem for a system of ordinary differential equations with parameters is constructed using the fundamental matrix of the differential equation. A system of linear algebraic equations for the parameters is compiled using the values of the solution at the corresponding points and substituting them into the two-point condition, the continuity condition, and the conditions for the piecewise constant argument. A modification of Dzhumabaev parameterization method for solving the considering boundary value problem is proposed which is based on solving the constructed system and the 4th order Runge-Kutta method for solving the Cauchy problem on subintervals. The obtained results are verified by a numerical example. Numerical analysis showed high efficiency of the constructed modification of Dzhumabaev parameterization method.Цитирования (OpenAlex) 4Цитирования (OpenCitations) 2