Four-Point Optimal Sixteenth-Order Iterative Method for Solving Nonlinear Equations

Abstract

We present an iterative method for solving nonlinear equations. The proposed iterative method has optimal order of convergence sixteen in the sense of Kung-Traub conjecture (Kung and Traub, 1974); it means that the iterative scheme uses five functional evaluations to achieve 16(=$2^{5-1}$) order of convergence. The proposed iterative method utilizes one derivative and four function evaluations. Numerical experiments are made to demonstrate the convergence and validation of the iterative method.