Families of Iterative Methods with Higher Convergence Orders for Solving Nonlinear Equations

Abstract

Recently, there has been progress in developing Newton-type methods with higher convergence to solve nonlinear equations. This paper develops new classes of iterative methods with higher convergence orders (more than four) by a construction of two iterative methods of integer-order of convergence,  and . The construction of such methods provides new classes of methods of order  of convergence. Numerical examples are provided, as well as the use of other existing methods to demonstrate the performance of the presented methods.