Complex dynamics of a sixth and seventh order family of root finding methods

Abstract

This paper intends to investigate the dynamical behavior of a parameter based sixth and seventh order convergent family of iterative methods in the complex plane. The fixed points of the rational function obtained from this family are described with their stability. Further to this, the stability regions for the fixed points are displayed using graphical tools. Parameter planes for independent free critical points are presented to determine stable and poor members of the family. Dynamical planes are also provided for various iterative methods of the family having important numerical properties.