Title: A new approach to study the dynamics of the modified Newton’s method to multiple roots
Author: Cadenas Román, Carlos Eduardo
Abstract: A new approach to study the dynamics of the Modified Newton’s method due to Schr¨oder is presented. This is a very simple but general approach that allows the study of the dynamics of methods to solve nonlinear equations, particularly when these have two roots with different multiplicity. Then, using the classical procedure to study the dynamics of iterative methods in the Riemann sphere, the stability of the fixed points and the parameter space associated with the critical point obtained are studied. Finally, dynamical planes and basins of attraction that confirm the results are shown.
