A slight generalization of Steffensen Method for Solving Non Linear Equations

Abstract

In this article, we present an iterative method to find simple roots of nonlinear equations, that is, to solving an equation of  the  form  f (x)  =  0.  Different  from  Newton’s method, the method we purpose do not require evaluation of derivatives. The method is based on the classical Steffensen’s method and it is a slight modification of it. The proofs of theoretical results are stated using Landau’s Little o notation and simples concepts of Real Analysis.  We prove that the method converges and its rate of convergence is quadratic. The method present some advantages when compared with Newton’s and Steffesen’s methods as illustrated by numerical tests given.

Mathematics subject classification: 65-02, 65-11, 65B99

DOI: https://doi.org/10.56238/tfisdwv1-142