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A Numerical Method for Solving Ordinary Differential Equations by Converting Them into the Form of a Shannon

Authors
  • Chikurov, N. G.1
  • 1 Ufa State Aviation Technical University, Ufa, Russia , Ufa (Russia)
Type
Published Article
Journal
Mathematical Models and Computer Simulations
Publisher
Pleiades Publishing
Publication Date
Mar 01, 2021
Volume
13
Issue
2
Pages
274–285
Identifiers
DOI: 10.1134/S2070048221020058
Source
Springer Nature
Keywords
License
Yellow

Abstract

AbstractA 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 sufficient 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.

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