An Optimal Class of Fourth-order Iterative Methods without Restraint on the First Derivative

Abstract

In an attempt to create an iterative method that may converge even if the first derivative disappears during the recursive process. This paper sets out to develop a class of optimal fourth-order methods based on Wu's modified Newton scheme for solving nonlinear equations without constraints on the first derivative. Numerous numerical examples were given to demonstrate how effectively the proposed methods perform. In addition, the basins of attraction confirm the efficiency and performance of the suggested fourth-order method compared with some other fourth-order schemes.