ANALYSIS OF R\"{O}SSLER ATTRACTOR BY MEANS OF RESIDUAL AND JOUBERT-GREEFF METHODS

Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 79

Volume : 19 , Issue : 2
DOI: https://doi.org/10.56827/SEAJMMS.2023.1902.32
Author :
M. C. Kekana (Tshwane University of Technology, Arcadia Campus, Pretoria, SOUTH AFRICA )
M. Y. Shatalov (Tshwane University of Technology, Arcadia Campus, Pretoria, SOUTH AFRICA )
T.O Tong (Tshwane University of Technology, Arcadia Campus, Pretoria, SOUTH AFRICA )
S. E. Fadugba (Department of Mathematics, Ekiti State University, Ado Ekiti, NIGERIA)

Abstract

In this paper, A mathematical framework of checking accuracy of numerical methods from mathematical software is been developed and investigated. R\"{o}ssler attractor is used as case study as its analytical solution is non-existence. The algorithms investigated from Mathcad software includes AdamsBDF, Adams, BDF and Runge-Kutta fixed methods. The numerical solutions of each built-in algorithms are compared to well-known Joubert-Greeff method. The estimation of global and local residuals are shown. The graphical results are plotted on an interval of 0 $\le$ t $\le$ 150.

Keywords and Phrases

R\"{o}ssler attractor , MathCad software, Joubert-Greeff method , global and local residuals.

A.M.S. subject classification

74H15, 45G10, 65D32, 65D30, 65G99.

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