On a New Efficient Steffensen-Like Iterative Class by Applying a Suitable Self-Accelerator Parameter

It is attempted to present an efficient and free derivative class of Steffensen-like methods for solving nonlinear equations. To this end, firstly, we construct an optimal eighth-order three-step uniparameter without memory of iterative methods. Then the self-accelerator parameter is estimated using Newton’sinterpolation in such a way that it improves its convergence order from 8 to 12 without any extra function evaluation. Therefore, its efficiency index is increased from 81/4 to 121/4 which is the main feature of this class. To show applicability of the proposed methods, some numerical illustrations are presented.