NUMERICAL SOLUTION OF A BOUNDARY VALUE PROBLEM WITH A PARAMETER FOR IMPULSIVE LOADED DIFFERENTIAL EQUATIONS

ИМПУЛЬСТІ ЖҮКТЕЛГЕН ДИФФЕРЕНЦИАЛДЫҚ ТЕҢДЕУЛЕР ҮШІН ПАРАМЕТРЛІ ШЕТТІК ЕСЕПТІ САНДЫҚ ШЕШУ
ЧИСЛЕННОЕ РЕШЕНИЕ КРАЕВОЙ ЗАДАЧИ С ПАРАМЕТРОМ ДЛЯ ИМПУЛЬСНЫХ НАГРУЖЕННЫХ ДИФФЕРЕНЦИАЛЬНЫХ УРАВНЕНИЙ
Кadirbayeva Z.М. Тemesheva S.М. Мinglibayeva B.B. Shaimerden N.М.
2024 Kazakh-British Technical University

Herald of the Kazakh British Technical UNiversity
2024 #21 Issue 2 106 - 115 pp.

The boundary value problem depending on the parameter for the system of impulsive loaded differential equations is considered. Algorithms of numerical realization of the Dzhumabaev parameterization method are developed for numerical solving of the studied boundary value problem depending on the parameter. Algorithms of numerical realization of the Dzhumabaev parameterization method are based on the solving of Cauchy problems for the system of ordinary differential equations. As a result of application of the proposed method, finding a solution to the boundary value problem depending on the parameter for impulsive loaded differential equations leads to finding a solution to the system of algebraic equations. This system of algebraic equations consists of a boundary condition and equalities with respect to the conditions at the impulsive points. Numerical results showing the high efficiency of the numerical implementation of the Dzhumabaev parameterization method are given. The result demonstrate that there is congruence between the numerical and the exact results to a high order of accuracy.

boundary value problem , impulse effect , loaded differential equation , parametrization method

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Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
International Information Technology University, Almaty, 050040, Kazakhstan
Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
Kazakh National Womens Teacher Training University, Almaty, 050000, Kazakhstan

Institute of Mathematics and Mathematical Modeling
International Information Technology University
Al-Farabi Kazakh National University
Kazakh National Womens Teacher Training University

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