Complex dynamics of derivative-free methods for nonlinear equations

The dynamical behavior of two iterative derivative-free schemes, Steffensen and M4 methods, is studied in case of quadratic and cubic polynomials. The parameter plane is analyzed for both procedures on quadratic polynomials. Different dynamical planes are showed when the mentioned methods are applied on particular cubic polynomials with real or complex coefficients. The property of immersion of the basins of attraction in all cases is analyzed. 2013 Elsevier Inc. All rights reserved.This research was supported by Ministerio de Ciencia y Tecnologia MTM2011-28636-C02-02 and by Vicerrectorado de Investigacion, Universitat Politecnica de Valencia PAID-06-2010-2285.Chicharro López, FI.; Cordero Barbero, A.; Gutiérrez, JM.; Torregrosa Sánchez, JR. (2013). Complex dynamics of derivative-free methods for nonlinear equations. Applied Mathematics and Computation. 219(12):7023-7035. doi:10.1016/j.amc.2012.12.075S702370352191