Abstract:
A new approach to study the dynamics of the Modified Newton's method due to Schröder 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.
Key Words: Nonlinear equations, modified Newton's method, dynamics, multiple roots.
2010 Mathematics Subject Classification: Primary 65H05.
