title: On a new efficient Steffensen-like iterative class by applying a suitable self-accelerator parameter.
abstract: 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.
authors.affiliation: Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan 68138, Iran.
authors.forename: Taher
authors.initials: T
authors.lastname: Lotfi
authors.affiliation: Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan 68138, Iran.
authors.forename: Elahe
authors.identifier: 0000-0001-5680-8509
authors.initials: E
authors.lastname: Tavakoli
mesh_terms: D000465:Algorithms; D008962:Models, Theoretical