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Zh. Vychisl. Mat. Mat. Fiz., 2019, Volume 59, Number 4, Pages 579–586 (Mi zvmmf10876)  

Approximate solution of differential equations with the help of rational spline functions

V. G. Magomedovaa, A.-R. K. Ramazanovab

a Dagestan State University, Makhachkala, Dagestan, 367000 Russia
b Dagestan Scientific Center, Russian Academy of Sciences, Makhachkala, Dagestan, 367032 Russia

Abstract: For twice continuously differentiable functions on an interval and for their derivatives up to the second order, estimates are obtained for their joint uniform approximations by rational interpolation splines and their corresponding derivatives. These estimates are used to construct approximate twice differentiable solutions of boundary value problems and an initial value problem for some second-order linear differential equations.

Key words: rational spline functions, interpolation spline functions, approximate solutions of differential equations.

DOI: https://doi.org/10.1134/S0044466919040112


English version:
Computational Mathematics and Mathematical Physics, 2019, 59:4, 542–549

Bibliographic databases:

UDC: 519.65
Received: 08.10.2018
Revised: 12.12.2018
Accepted:12.12.2018

Citation: V. G. Magomedova, A.-R. K. Ramazanov, “Approximate solution of differential equations with the help of rational spline functions”, Zh. Vychisl. Mat. Mat. Fiz., 59:4 (2019), 579–586; Comput. Math. Math. Phys., 59:4 (2019), 542–549

Citation in format AMSBIB
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