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 ۲;۴;۸,and ۲^n to ۳.۵,۷,۱۴;and ۳.۵*۲^n-۱,respectively without any extra evaluation.Computational results confirm the efficient and robust character of presented methods.

Keywords:

Nonlinear equations , With memory methods , Acceleration of convergence , Efficiency index