2020/11/26 by Gutiérrez, José M., Galilea, Víctor
#Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.2011.13308
The purpose of this work is to give a first approach to the dynamical behavior of Schröder's method, a well known iterative process for solving nonlinear equations. In this context we consider equations defined in the complex plane. By using topological conjugations, we characterize the basins of attraction of Schröder's method applied to polynomials with two roots and different multiplicities. Actually, we show that these basins are half-planes or circles, depending on the multiplicities of the roots. We finish our study with a graphical gallery that allow us to compare the basins of attraction of Newton's and Schröoder's method applied to some given polynomials. Key: Schröder's method; basin of attraction; nonlinear equation.