A second derivative-free eighth-order nonlinear equation solver

Abstract

Finding the simple roots of nonlinear equations is a classical problem of numerical analysis which has lots of applications in many sciences and engineering branches. In this paper, we obtain an efficient eighth-order iterative scheme without memory by using a third-order iterative scheme  also known as the method of Weerakoon and Fernando. The proposed simple root solver includes three evaluations of the function and two evaluations of the first derivative per iteration, which implies 1.516 as its efficiency index. Several numerical instances are included, and the obtained results recommend that this iterative scheme introduces a favorable tool for solving single variable nonlinear equations, where the computational (operational) index is better in contrast to the existing high-order methods in the literature.