Numerical Solution of Second‐Order Impulsive Differential Equations With Loadings Subject to Integral Boundary Conditions

ABSTRACT In this paper, we present a computational method for solving the second‐order impulsive differential equations with loadings subject to integral boundary conditions based on the Dzhumabaev parametrization method. The idea of this method involves introducing additional parameters, reducing t...

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Bibliographic Details
Published inMathematical methods in the applied sciences Vol. 48; no. 6; pp. 6269 - 6277
Main Authors Kadirbayeva, Zhazira, Kadirbayeva, Roza
Format Journal Article
LanguageEnglish
Published Freiburg Wiley Subscription Services, Inc 01.04.2025
Subjects
Boundary conditions
Cauchy problems
Differential equations
impulsive differential equations
integral conditions
Linear algebra
loadings
numerical algorithm
Parameterization
parametrization method
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Summary:ABSTRACT In this paper, we present a computational method for solving the second‐order impulsive differential equations with loadings subject to integral boundary conditions based on the Dzhumabaev parametrization method. The idea of this method involves introducing additional parameters, reducing the original problem to solving a system of linear algebraic equations. The system's coefficients and right‐hand side are determined by solving Cauchy problems for ODEs and by calculating definite integrals. Four examples are provided to show the effectiveness and feasibility of the main results.
Bibliography:Funding
This research is funded by the Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan (Grant No. AP19675193).
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ISSN:0170-4214
1099-1476
DOI:10.1002/mma.10670