Basins of Attraction for Various Steffensen-Type Methods | Zendy

Alicia Cordero | Zendy; Fazlollah Soleymani | Zendy; Juan R. Torregrosa | Zendy; Stanford Shateyi | Zendy

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Basins of Attraction for Various Steffensen-Type Methods

Author(s) -

Alicia Cordero,

Fazlollah Soleymani,

Juan R. Torregrosa,

Stanford Shateyi

Publication year - 2014

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2014/539707

Subject(s) - convergence (economics) , type (biology) , chaotic , mathematics , computer science , steffensen's method , fixed point , derivative (finance) , stability (learning theory) , attraction , local convergence , algorithm , mathematical optimization , mathematical analysis , iterative method , geology , artificial intelligence , newton's method in optimization , paleontology , linguistics , philosophy , machine learning , economic growth , financial economics , economics

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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