%0 Journal Article
%J International Journal of Bifurcation and Chaos (IJBC)
%D 2011
%T Studying the basin of convergence of methods for computing periodic orbits
%A M. G. Epitropakis
%A M. N. Vrahatis
%X 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 â„‚, 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 PoincarĂ© map on a surface of section.
%B International Journal of Bifurcation and Chaos (IJBC)
%V 21
%P 1-28
%G eng
%R 10.1142/S0218127411029653