Fourth-order family of iterative methods with four parameters

Abstract

We present a novel fourth order convergent family of iterative methods, consisting of four parameters, for solving nonlinear scalar equations. Methods require evaluations of two functions and one-derivative per iteration and methods are free from second and higher-order derivatives. Convergence analysis shows that the family is fourth-order convergent. Computational results demonstrate that the family of methods are efficient and demonstrate equal or better performance as compared with other well known methods. Numerical experiments show that methods may converge even if the derivative vanishes during the iterative process and methods are converging for a wide range of initializations.