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2014 Basins of Attraction for Various Steffensen-Type Methods
Alicia Cordero, Fazlollah Soleymani, Juan R. Torregrosa, Stanford Shateyi
J. Appl. Math. 2014: 1-17 (2014). DOI: 10.1155/2014/539707

Abstract

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.

Citation

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Alicia Cordero. Fazlollah Soleymani. Juan R. Torregrosa. Stanford Shateyi. "Basins of Attraction for Various Steffensen-Type Methods." J. Appl. Math. 2014 1 - 17, 2014. https://doi.org/10.1155/2014/539707

Information

Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07010674
MathSciNet: MR3191125
Digital Object Identifier: 10.1155/2014/539707

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
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