Eight and ninth-order convergence iterative structures for obtaining nonlinear equations solution

Abstract

An eighth and ninth-order fast convergence iterative structures for determining the solution of nonlinear equations is put forward in this manuscript. The iterative structures are modification of a three-step variants of the Newton method via the use of the divided deference and weight functions. The computational iterative structures possess the advantages that they, do not require evaluation of higher derivative and converge faster than compared iterative structures with same convergence order. The convergence analysis of the iterative structures was established via the method of Taylor series. The computational results obtained with the developed iterative structures are juxtaposed with those obtained from some contemporary existing methods, and they performed better in terms of fast convergence.