Basins of attraction for various Steffensen-type methods
type: Item
instance of: scholarly article
title: Basins of attraction for various Steffensen-type methods
zbMATH Open document ID: 1406.65035
DOI: 10.1155/2014/539707
author: Alicia Cordero
author: Fazlollah Soleymani
author: S. Shateyi
author: Juan Ramón Torregrosa Sánchez
published in: Journal of Applied Mathematics
publication date: 2019-02-01T00:00:00Z
review text: Summary: The dynamical behavior of different Steffensen-type methods is analyzed. We check the chaotic behaviors alongside the convergence radii (understood as the wideness of the basin of attraction) needed by Steffensen-type methods, that is, derivative-free iteration functions, to converge to a root and compare the results using different numerical tests. We will conclude that the convergence radii (and the stability) of Steffensen-type methods are improved by increasing the convergence order. The computer programming package MATHEMATICA provides a powerful but easy environment for all aspects of numerics. This paper puts on show one of the application of this computer algebra system in finding fixed points of iteration functions.
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 7010674
Wikidata QID: Q59053456
describes a project that uses: Mathematica
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/539707
OpenAlex ID: W2024423464
description: scientific article; zbMATH DE number 7010674