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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

An Accurate Numerical Method and Algorithm for Constructing Solutions of Chaotic Systems

Journal of Applied Nonlinear Dynamics 9(2) (2020) 207--221 | DOI:10.5890/JAND.2020.06.004

Alexander N. Pchelintsev

Department of Higher Mathematics, Tambov State Technical University, ul. Sovetskaya 106, Tambov, 392000, Russia

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Abstract

In various fields of natural science, the chaotic systems of differential equations are considered more than 50 years. The correct prediction of the behaviour of solutions of dynamical model equations is important in understanding of evolution process and reduce uncertainty. However, often used numerical methods are unable to do it on large time segments. In this article, the author considers the modern numerical method and algorithm for constructing solutions of chaotic systems on the example of tumor growth model. Also a modification of Benettin’s algorithm presents for calculation of Lyapunov exponents.

Acknowledgments

The reported study was funded by RFBR according to the research project 20-01-00347.

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