A New Efficient Optimal Eighth-Order Iterative Method for Solving Nonlinear Equations

TL;DR

This paper introduces a new eighth-order iterative method for solving nonlinear equations that is efficient, requiring only four evaluations per iteration, and demonstrates superior performance over existing methods.

Contribution

The paper presents a novel eighth-order iterative method with a three-step process that improves efficiency and convergence for solving nonlinear equations.

Findings

Achieves eighth-order convergence

Requires four evaluations per iteration

Outperforms existing eighth-order methods in tests

Abstract

We established a new eighth-order iterative method, consisting of three steps, for solving nonlinear equations. Per iteration the method requires four evaluations (three function evaluations and one evaluation of the first derivative). Convergence analysis shows that this method is eighth-order convergent which is also substantiated through the numerical works.Computational results ascertain that our method is efficient and demonstrate almost better performance as compared to the other well known eighth-order methods.