Abstract
A linear two-point boundary value problem for a system of loaded differential equations with impulse effect is investigated. Values in the previous impulse points are taken into consideration in the conditions of impulse effect. The considered problem is reduced to an equivalent multi-point boundary value problem for the system of ordinary differential equations with parameters. A numerical implementation of parametrization method is offered using the Runge–Kutta method of 4th-order accuracy for solving the Cauchy problems for ordinary differential equations. The constructed numerical algorithms are illustrated by examples.
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Acknowledgements
The results partially supported by Grants No.0822/\(\Gamma \Phi 4\) and No. AP05131220 of Ministry education and Science of the Republic of Kazakhstan. The authors thank the referees for their careful reading of our manuscript and for giving the constructive comments, which substantially helped to improve the quality of the paper.
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Communicated by Jorge X. Velasco.
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Assanova, A.T., Kadirbayeva, Z.M. On the numerical algorithms of parametrization method for solving a two-point boundary-value problem for impulsive systems of loaded differential equations. Comp. Appl. Math. 37, 4966–4976 (2018). https://doi.org/10.1007/s40314-018-0611-9
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DOI: https://doi.org/10.1007/s40314-018-0611-9