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Abstract and Applied Analysis
Volume 2015, Article ID 289029, 12 pages
Research Article

Design of High-Order Iterative Methods for Nonlinear Systems by Using Weight Function Procedure

1Instituto Tecnológico de Santo Domingo (INTEC), Avenida Los Próceres, Galá, 10602 Santo Domingo, Dominican Republic
2Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 València, Spain

Received 9 September 2014; Accepted 25 November 2014

Academic Editor: Benito M. Chen-Charpentier

Copyright © 2015 Santiago 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.


We present two classes of iterative methods whose orders of convergence are four and five, respectively, for solving systems of nonlinear equations, by using the technique of weight functions in each step. Moreover, we show an extension to higher order, adding only one functional evaluation of the vectorial nonlinear function. We perform numerical tests to compare the proposed methods with other schemes in the literature and test their effectiveness on specific nonlinear problems. Moreover, some real basins of attraction are analyzed in order to check the relation between the order of convergence and the set of convergent starting points.