Some new families of fifth -order methods for finding simple zeros of non-linear equations

Abstract

In this paper, we developed some new families of fth-order methods for solving simple zerosof non-linear equations. This new family of methods is constructed such that the convergence is of orderve. Each member of the families requires two evaluations of the given function and two of its derivativeper iteration. These methods have more advantages than Newtons method and other methods with thesame convergence order, as shown in the illustration examples.