A class of efficient derivative free iterative method with and without memory for solving nonlinear equations

Document Type : Regular paper


Faculty of Mathematics and Statistics, Malayer University, Malayer, Iran.


In the present paper, at first, we propose a new two-step iterative method for solving nonlinear equations. This scheme is based on the Steffensen's method, in which the order of convergence is four. This iterative method requires only three functions evaluation in each iteration, therefore it is optimal in the sense of the Kung and Traub conjecture. Then we extend it to the method with memory, which the order of convergence is six. Finally, numerical examples indicate that the
obtained methods in terms of accuracy and computational cost are superior to the
famous forth-order methods.


Volume 1, Issue 2 - Serial Number 2
December 2022
Pages 20-26
  • Receive Date: 19 August 2022
  • Revise Date: 16 September 2022
  • Accept Date: 21 September 2022
  • First Publish Date: 28 September 2022