  We use simple equations in order to compare the basins of attraction on the
complex plane, corresponding to a large collection of numerical methods, of
several order. Two cases are considered, regarding the total number of the
roots, which act as numerical attractors. For both cases we use the iterative
schemes for performing a thorough and systematic classification of the nodes on
the complex plane. The distributions of the required iterations as well as the
probability and their correlations with the corresponding basins of convergence
are also discussed. Our numerical calculations suggest that most of the
iterative schemes provide relatively similar convergence structures on the
complex plane. In addition, several aspects of the numerical methods are
compared in an attempt to obtain general conclusions regarding their speed and
efficiency. Moreover, we try to determine how the complexity of the each case
influences the main characteristics of the numerical methods.
