Studying the basin of convergence of methods for computing periodic orbits

Citation

Epitropakis M & Vrahatis MN (2011) Studying the basin of convergence of methods for computing periodic orbits. International Journal of Bifurcation and Chaos, 21 (8), pp. 2079-2106. https://doi.org/10.1142/S0218127411029653

Abstract
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.

Keywords
Structure of fractals; fractals; nonlinear dynamics; numerical methods (mathematics); periodic orbits of nonlinear mappings; fixed points of the Poincaré map

Journal
International Journal of Bifurcation and Chaos: Volume 21, Issue 8