On an Efficient Family with Memory with High Order of Convergence for Solving Nonlinear ‎Equations‎

The primary goal of this work is to introduce general family Steffensen-like methods with memory of the high efficiency indices.To achieve this target two parameters are introduced which are calculated with the help of Newton’s interpolatory polynomial.It is shown that the R-order convergence of the proposed methods has been increased from 2;4;8,... and 2^n to 3.5,7,14, ... and 3.5*2^n-1,respectively without any extra evaluation.Computational results confirm the efficient and robust character of presented methods.