Studying the basin of convergence of methods for computing periodic orbits

TitleStudying the basin of convergence of methods for computing periodic orbits
Publication TypeJournal Article
Year of Publication2011
AuthorsEpitropakis, MG, Vrahatis, MN
JournalInternational Journal of Bifurcation and Chaos (IJBC)
Volume21
Pagination1-28
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.

DOI10.1142/S0218127411029653
AttachmentSize
PDF icon EpitropakisVrahatis2011_IJBC.pdf3.34 MB

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