Abstract

In this paper, we suggest and analyze some new higher-order iterative methods free from second derivative for solving nonlinear equations. Per iteration, these new methods require three evaluations of the function and two of its first-derivative with efficiency index =   Convergence of their methods is also considered. Several numerical examples are given to illustrate the efficiency and performance of these new methods. These new iterative methods may be viewed as an alternative to the known methods.

Key words: Nonlinear equations, Newton method, convergence criteria, root finding method, numerical examples.