TY - JOUR
T1 - Studying the basin of convergence of methods for computing periodic orbits
JF - International Journal of Bifurcation and Chaos (IJBC)
Y1 - 2011
A1 - M. G. Epitropakis
A1 - M. N. Vrahatis
AB - 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.
VL - 21
ER -