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Journal of Applied Mathematics
Volume 2014, Article ID 591638, 9 pages
http://dx.doi.org/10.1155/2014/591638
Research Article

Optimal High-Order Methods for Solving Nonlinear Equations

1Instituto Tecnológico de Santo Domingo (INTEC), Avenida de Los Próceres, Galá, 10601 Santo Domingo, Dominican Republic
2Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 40022 Valencia, Spain

Received 4 February 2014; Accepted 7 April 2014; Published 5 May 2014

Academic Editor: Ioannis K. Argyros

Copyright © 2014 S. Artidiello 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.

Abstract

A class of optimal iterative methods for solving nonlinear equations is extended up to sixteenth-order of convergence. We design them by using the weight function technique, with functions of three variables. Some numerical tests are made in order to confirm the theoretical results and to compare the new methods with other known ones.