Steffensen type methods for solving nonlinear equations

In the present paper, by approximating the derivatives in the well known fourth-order Ostrowski’s method and in a sixth-order improved Ostrowski’s method by central-difference quotients, we obtain new modifications of these methods free from derivatives. We prove the important fact that the methods obtained preserve their convergence orders 4 and 6, respectively, without calculating any derivatives. Finally, numerical tests confirm the theoretical results and allow us to compare these variants with the corresponding methods that make use of derivatives and with the classical Newton’s method.