Stability of a Family of Iterative Methods of Fourth-Order

Abstract

In this paper, we analyze the dynamical anomalies of a family of iterative methods, for solving nonlinear equations, designed by using weight function procedure. All the elements of the family are optimal schemes (in the sense of Kung-Traub conjecture) of fourth-order, but not all have the same stability properties. So, we describe the dynamical behavior of this family on quadratic polynomials. The study of fixed points and their stability, joint with the critical points and their associated parameter planes, show the richness of the presented class and allow us to select the members of the family with good stability properties.