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Advanced Technologies in Robotics and Intelligent Systems pp 365–373Cite as

Application of a Computer Algebra System for Constructing Newton Polygons for Ordinary Differential Equations

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Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 80))

Abstract

Newton polygons corresponding to nonlinear ordinary differential equations of polynomial form help visually determine some properties of differential equations. In particular, the Newton polygons are used at finding asymptotic and exact solutions of nonlinear differential equations. In this report we present the algorithm of the ACNP (automatic construction of Newton polygons) program for the automatic construction of the Newton polygons corresponding to ordinary differential equations. The program has been written in Maple symbolic computing environment. The input to the program is a polynomial ordinary differential equation. The output is a set of points on the plane corresponding, according to a certain rule, to the monomials of the differential equation, the Newton polygon and the pole order of the solution for the differential equation. The application of the ACNP program has been demonstrated for studying the integrability property and for finding exact and asymptotic solutions of nonlinear differential equations.

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Acknowledgements

The study was carried out with a grant from the Russian Science Foundation (project No. 18-11-00209).

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Authors and Affiliations

  1. National Research Nuclear University MEPhI, Moscow, 115409, Russia

    N. A. Kudryashov & A. A. Kutukov

Authors
  1. N. A. Kudryashov
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  2. A. A. Kutukov
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Correspondence to A. A. Kutukov .

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Editors and Affiliations

  1. Institute of Cyber Intelligence Systems, National Research Nuclear University MEPhI, Moscow, Russia

    Sergey Yu. Misyurin

  2. LS2N, Institut National des Sciences Appliquées, Rennes, France

    Vigen Arakelian

  3. Institute for System Programming, Russian Academy of Sciences, Moscow, Russia

    Arutyun I. Avetisyan

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Kudryashov, N.A., Kutukov, A.A. (2020). Application of a Computer Algebra System for Constructing Newton Polygons for Ordinary Differential Equations. In: Misyurin, S., Arakelian, V., Avetisyan, A. (eds) Advanced Technologies in Robotics and Intelligent Systems. Mechanisms and Machine Science, vol 80. Springer, Cham. https://doi.org/10.1007/978-3-030-33491-8_44

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