A new family of iterative methods widening areas of convergence

Abstract

A new parametric class of third-order iterative methods for solving nonlinear equations and systems is presented. These schemes are showed to be more stable than Newton’, Traub’ or Ostrowski’s procedures (in some specific cases), and it has been proved that the set of starting points that converge to the roots of different nonlinear functions is wider than the one of those respective methods. Moreover, the numerical efficiency has been checked through different numerical tests.