NUMERICAL SOLUTION OF A BOUNDARY VALUE PROBLEM WITH A PARAMETER FOR IMPULSIVE LOADED DIFFERENTIAL EQUATIONS
https://doi.org/10.55452/1998-6688-2024-21-2-106-115
Abstract
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.
Keywords
Supporting agencies: Бұл зерттеуді Қазақстан Республикасының Ғылым және жоғары білім министрлігінің Ғылым комитеті (грант № AP19675193) қаржыландырады
About the Authors
Zh. M. Кadirbayeva
Institute of Mathematics and Mathematical Modeling; International Information Technology University
Kazakhstan
Kazakhstan
Candidate of Physical and Mathematical Sciences, Associate Professor
050010, Almaty
050040, Almaty
S. M. Тemesheva
Institute of Mathematics and Mathematical Modeling; Al-Farabi Kazakh National University
Kazakhstan
Kazakhstan
Doctor of Physical and Mathematical Sciences, Associate Professor
050010, Almaty
050040, Almaty
B. B. Мinglibayeva
Institute of Mathematics and Mathematical Modeling;
Kazakhstan
Kazakhstan
Candidate of Physical and Mathematical Sciences
050010, Almaty
N. M. Shaimerden
Kazakh National Women's Teacher Training University
Kazakhstan
Kazakhstan
Master
050000, Almaty
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Review
For citations:
Кadirbayeva Zh.M., Тemesheva S.M., Мinglibayeva B.B., Shaimerden N.M. NUMERICAL SOLUTION OF A BOUNDARY VALUE PROBLEM WITH A PARAMETER FOR IMPULSIVE LOADED DIFFERENTIAL EQUATIONS. Herald of the Kazakh-British technical university. 2024;21(2):106-115. (In Kazakh) https://doi.org/10.55452/1998-6688-2024-21-2-106-115
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