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Approximate Solution of Nonlinear Differential Equations with the Help of Rational Spline Functions

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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.

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Authors and Affiliations

  1. Dagestan State University, 367000, Makhachkala, Dagestan, Russia

    V. G. Magomedova & A.-R. K. Ramazanov

  2. Dagestan Scientific Center, Russian Academy of Sciences, 367032, Makhachkala, Dagestan, Russia

    A.-R. K. Ramazanov

Authors
  1. V. G. Magomedova
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  2. A.-R. K. Ramazanov
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Corresponding authors

Correspondence to V. G. Magomedova or A.-R. K. Ramazanov.

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Translated by I. Ruzanova

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Magomedova, V.G., Ramazanov, AR.K. Approximate Solution of Nonlinear Differential Equations with the Help of Rational Spline Functions. Comput. Math. and Math. Phys. 61, 1252–1259 (2021). https://doi.org/10.1134/S0965542521080042

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  • DOI: https://doi.org/10.1134/S0965542521080042

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