An Optimal Fourth Order Iterative Method for Solving Nonlinear Equations and Its Dynamics
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Date
2015
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Hindawi Publishing Corporation,Journal of Complex Analysis
Abstract
We present a new fourth order method for finding simple roots of a nonlinear equation 𝑓(𝑥) = 0. In terms of computational cost,
per iteration the method uses one evaluation of the function and two evaluations of its first derivative. Therefore, the method has
optimal order with efficiency index 1.587 which is better than efficiency index 1.414 of Newton method and the same with Jarratt
method and King’s family. Numerical examples are given to support that the method thus obtained is competitive with other similar
robust methods. The conjugacy maps and extraneous fixed points of the presented method and other existing fourth order methods
are discussed, and their basins of attraction are also given to demonstrate their dynamical behavior in the complex plane.