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

License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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’s interpolation 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. 1