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Title

Basins of Attraction for Various Steffensen-Type Methods
Authors

Alicia Cordero
Organization: Instituto de Matem´atica Multidisciplinar, Universitat Polit`ecnica de Val`encia
Fazlollah Soleymani
Organization: Department of Mathematics, Islamic Azad University
J. R. Torregrosa
Organization: Instituto de Matem´atica Multidisciplinar, Universitat Polit`ecnica de Val`encia
Stanford Shateyi
Organization: Department of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda
Journal / Anthology

Journal of Applied Mathematics
Year: 2014
Volume: 2014
Description

Thedynamical behavior of different Steffensen-typemethods 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-typemethods 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.
Subject

*Applied Mathematics


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