Қазақ ұлттық қыздар педагогикалық университеті / Казахский национальный женский педагогический университет

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    On one algorithm for finding a solution to a two-point boundary value problem for loaded differential equations with impulse effect
    (Karaganda Buketov University, 2017-09-30)
    E. А. Bakirova
    ;
    Zh. М. Каdirbayeva
    ;
    Agila B. Tleulessova
    On 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
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    NUMERICAL IMPLEMENTATION FOR SOLVING THE BOUNDARY VALUE PROBLEM FOR IMPULSIVE INTEGRO-DIFFERENTIAL EQUATIONS WITH PARAMETER
    (Al-Farabi Kazakh National University, 2023-10-17)
    E. А. Bakirova
    ;
    N. Iskakova
    ;
    Zh. Kadirbayeva
    In 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