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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.

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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

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