<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">M. G. Epitropakis</style></author><author><style face="normal" font="default" size="100%">M. N. Vrahatis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Studying the basin of convergence of methods for computing periodic orbits</style></title><secondary-title><style face="normal" font="default" size="100%">International Journal of Bifurcation and Chaos (IJBC)</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2011</style></year></dates><volume><style face="normal" font="default" size="100%">21</style></volume><pages><style face="normal" font="default" size="100%">1-28</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">Starting from the well-known Newton's fractal which is formed by the basin of convergence of Newton's method applied to a cubic equation in one variable in the field ℂ, we were able to find methods for which the corresponding basins of convergence do not exhibit a fractal-like structure. Using this approach we are able to distinguish reliable and robust methods for tackling a specific problem. Also, our approach is illustrated here for methods for computing periodic orbits of nonlinear mappings as well as for fixed points of the Poincaré map on a surface of section.</style></abstract></record></records></xml>