On developing a new three accelerators iterative method for solving nonlinear equation

In this study, based on the first three steps of the optimal iterative method without memory introduced by Zheng et al. [16], we develop a new three accelerators method with memory for approximating a simple zero of a nonlinear equation. To this end, we introduce three parameters and try to update them in each iteration so that without any new function evaluations the convergence order increases from eight to fifteen.This is the primal goal of this work. Theoretical and numerical discussions for the proposed method are given.

Keywords:

Nonlinear equation , Method with memory , R-order of convergence , Self-accelerating parameter , Efficiency index