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Mathematical Problems in Engineering
Volume 2011, Article ID 469512, 10 pages
Research Article

A General Three-Step Class of Optimal Iterations for Nonlinear Equations

1Young Researchers Club, Islamic Azad University, Zahedan Branch, Zahedan 98168, Iran
2Department of Mathematics, Islamic Azad University, Zahedan Branch, Zahedan 98168, Iran

Received 7 August 2011; Accepted 16 September 2011

Academic Editor: Hung Nguyen-Xuan

Copyright © 2011 Fazlollah Soleymani et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Many of the engineering problems are reduced to solve a nonlinear equation numerically, and as a result, an especial attention to suggest efficient and accurate root solvers is given in literature. Inspired and motivated by the research going on in this area, this paper establishes an efficient general class of root solvers, where per computing step, three evaluations of the function and one evaluation of the first-order derivative are used to achieve the optimal order of convergence eight. The without-memory methods from the developed class possess the optimal efficiency index 1.682. In order to show the applicability and validity of the class, some numerical examples are discussed.