ANALYSIS OF R¨OSSLER ATTRACTOR BY MEANS OF RESIDUAL AND JOUBERT-GREEFF METHODS

M.C Kekana; M.Y Shatalov; T.O Tong; S.E Fadugba

doi:10.56827/SEAJMMS.2023.1902.32

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

DOI: https://doi.org/10.56827/SEAJMMS.2023.1902.32

Keywords: R¨ossler attractor , MathCad software, Joubert-Greeff method , global and local residuals.

Abstract

In this paper, A mathematical framework of checking accuracy of numerical methods from mathematical software is been developed and investigated. R¨ossler 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 < t < 150.