A Novel and Precise Sixth-Order Method for Solving Nonlinear Equations

This study presents a novel and robust three-step sixthorder iterative scheme for solving nonlinear equations. The contributed without memory method includes two evaluations of the function and two evaluations of the first derivative per iteration which implies 1.565 as its efficiency index. Its theoretical proof is furnished to show the error equation. The most important merits of the novel method are as follows. First in numerical problems, the developed scheme mostly performs better or equal in contrast with the optimal eighth-order methods, such as [7] when the initial guesses are not so close to the sought zeros. Second, its convergence radius is more than the convergence radii of the optimal eighth-order methods. Third, its (extended) computational (operational) index is better in comparison with optimal eighth-order methods. That is, besides the high accuracy and bigger convergence radius in numerical examples for not so close starting points; our method has less computational complexity as well.