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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 8 1/4  to 12 1/4  which is the main feature of this class. To show applicability of the proposed methods, some numerical illustrations are presented.

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