A Family of Optimal Derivative Free Iterative Methods with Eighth-Order Convergence for Solving Nonlinear Equations

Abstract

In this paper, modification of Steffensen’s method with eight-order convergence is presented. We propose a family of optimalthree-step methods with eight-order convergence for solving the simpleroots of nonlinear equations by using the weight function and interpolationmethods. Per iteration this method requires four evaluations of thefunction which implies that the efficiency index of the developed methodsis 1.682. Some numerical examples illustrate that the algorithm ismore efficient and performs better than other methods.