Application of the Euler and Runge–Kutta Generalized Methods for FDE and Symbolic Packages in the Analysis of Some Fractional Attractors-Reference-Cited by-同舟云学术

Application of the Euler and Runge–Kutta Generalized Methods for FDE and Symbolic Packages in the Analysis of Some Fractional Attractors

Published:2019-10-25 Issue:2 Volume:21 Page:159-170
ISSN:2191-0294
Container-title:International Journal of Nonlinear Sciences and Numerical Simulation
language:en
Short-container-title:

Author:

Milici Constantin¹,Tenreiro Machado José²^ORCID,Drăgănescu Gheorghe³

Affiliation:

1. Department of Mathematics , Polytechnic University of Timişoara , Timisoara , Romania

2. Department of Electrical Engineering , Institute of Engineering, Polytechnic of Porto , R. Dr. António Bernardino de Almeida, 431 , Porto 4249-015 , Portugal

3. Research Center in Theoretical Physics , West University of Timişoara , Timisoara , Romania

Abstract

Abstract This paper applies the Euler and the fourth-order Runge–Kutta methods in the analysis of fractional order dynamical systems. In order to illustrate the two techniques, the numerical algorithms are applied in the solution of several fractional attractors, namely the Lorenz, Duffing and Liu systems. The algorithms are implemented with the aid of Mathematica symbolic package. Furthermore, the Lyapunov exponent is obtained based on the Euler method and applied with the Lorenz fractional attractor.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Physics and Astronomy,Mechanics of Materials,Engineering (miscellaneous),Modeling and Simulation,Computational Mechanics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ijnsns-2018-0248/pdf

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