Basins of attraction for various steffensen-type methods

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. © 2014 alicia cordero et al.