Abstract: The main focus of this manuscript is to provide a
highly efficient two-point sixth-order family of super-Halley type
methods that do not require any second-order derivative evaluation
for obtaining simple roots of nonlinear equations, numerically. Each
member of the proposed family requires two evaluations of the given
function and two evaluations of the first-order derivative per iteration.
By using Mathematica-9 with its high precision compatibility, a
variety of concrete numerical experiments and relevant results are
extensively treated to confirm t he t heoretical d evelopment. From
their basins of attraction, it has been observed that the proposed
methods have better stability and robustness as compared to the other
sixth-order methods available in the literature.
Abstract: For the last years, the variants of the Newton-s method with cubic convergence have become popular iterative methods to find approximate solutions to the roots of non-linear equations. These methods both enjoy cubic convergence at simple roots and do not require the evaluation of second order derivatives. In this paper, we present a new Newton-s method based on contra harmonic mean with cubically convergent. Numerical examples show that the new method can compete with the classical Newton's method.