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Matem. Mod., 2020, Volume 32, Number 8, Pages 3–20 (Mi mm4202)  

A numerical method for solving ordinary differential equations by converting them into the form of a Shannon

N. G. Chikurov

Ufa State Aviation Technical University

Abstract: A numerical solution method based on the reduction of systems of ordinary differential equations to the Shannon form is considered. Shannon's equations differ in that they contain only multiplication and summation operations. The absence of functional transformations makes it possible to simplify and unify the process of numerical integration of differential equations in the form of Shannon. To do this, it is enough in the initial equations given in the normal form of Cauchy to make a simple replacement of variables. In contrast to the classical fourth-order Runge-Kutta method, the numerical method under consideration may have a higher order of accuracy.

Keywords: numerical methods, order of accuracy, ordinary differential equations, Shannon equations.

DOI: https://doi.org/10.20948/mm-2020-08-01

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Received: 12.08.2019
Revised: 09.01.2020
Accepted:27.01.2020

Citation: N. G. Chikurov, “A numerical method for solving ordinary differential equations by converting them into the form of a Shannon”, Matem. Mod., 32:8 (2020), 3–20

Citation in format AMSBIB
\Bibitem{Chi20}
\by N.~G.~Chikurov
\paper A numerical method for solving ordinary differential equations by converting them into the form of a Shannon
\jour Matem. Mod.
\yr 2020
\vol 32
\issue 8
\pages 3--20
\mathnet{http://mi.mathnet.ru/mm4202}
\crossref{https://doi.org/10.20948/mm-2020-08-01}


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