Basins of Attraction for Various Steffensen-Type Methods
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Alicia Cordero, Fazlollah Soleymani, Juan R. Torregrosa, Stanford Shateyi
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 M<jats:sc>ATHEMATICA</jats:sc>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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