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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2021, Volume 61, Number 8, Pages 1269–1277
DOI: https://doi.org/10.31857/S0044466921080044 (Mi zvmmf11274) 		 
Ordinary differential equations

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

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

a Dagestan State University, 367000, Makhachkala, Dagestan, Russia
b Daghestan Scientific Centre of Russian Academy of Sciences, Makhachkala
DOI: https://doi.org/10.31857/S0044466921080044
Abstract: A method for constructing an approximate solution in the form of a rational spline function is proposed for initial value problems in the case of first- and second-order differential equations solvable for the highest derivative. A spline function of this type is constructed via the transition to a system of scalar equations that is reduced to solving at most one nonlinear equation with one unknown and to making sequential substitutions of previously determined values.
Key words: rational spline functions, interpolation spline functions, approximate solution of differential equations.
Received: 07.08.2020
Revised: 08.11.2020
Accepted: 11.02.2021
English version:
Computational Mathematics and Mathematical Physics, 2021, Volume 61, Issue 8, Pages 1252–1259
DOI: https://doi.org/10.1134/S0965542521080042
Bibliographic databases:
Document Type: Article
UDC: 519.65
Language: Russian
Citation: V. G. Magomedova, A.-R. K. Ramazanov, “Approximate solution of nonlinear differential equations with the help of rational spline functions”, Zh. Vychisl. Mat. Mat. Fiz., 61:8 (2021), 1269–1277; Comput. Math. Math. Phys., 61:8 (2021), 1252–1259
Citation in format AMSBIB
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\paper Approximate solution of nonlinear differential equations with the help of rational spline functions
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\vol 61
\issue 8
\pages 1269--1277
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\jour Comput. Math. Math. Phys.
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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