Basins of Attraction for Various Steffensen-Type Methods

الملخص EN

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.