A family of Newton-Halley type methods to find simple roots of nonlinear equations and their dynamics

Abstract

In this work, a new family of Newton-Chebyshev type methods for solving nonlinear equations is presented. The dynamics of the Newton-Chebyshev family for the class of quadratic polynomials is analyzed and the convergence is established. We find the fixed and critical points. The stable and unstable behaviors are studied. The parameter space associated with the family is studied and finally, some dynamical planes that show different aspects of the dynamics of this family are presented.