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Journal of Applied Mathematics
Volume 2012, Article ID 709843, 15 pages
http://dx.doi.org/10.1155/2012/709843
Research Article

New Predictor-Corrector Methods with High Efficiency for Solving Nonlinear Systems

1Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera S/N, 40022 Valencia, Spain
2Instituto Tecnológico de Santo Domingo (INTEC), avenida de Los Próceres, Galóa, 10602 Santo Domingo, Dominican Republic

Received 20 July 2012; Revised 27 August 2012; Accepted 1 September 2012

Academic Editor: Fazlollah Soleymani

Copyright © 2012 Alicia Cordero 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 new set of predictor-corrector iterative methods with increasing order of convergence is proposed in order to estimate the solution of nonlinear systems. Our aim is to achieve high order of convergence with few Jacobian and/or functional evaluations. Moreover, we pay special attention to the number of linear systems to be solved in the process, with different matrices of coefficients. On the other hand, by applying the pseudocomposition technique on each proposed scheme we get to increase their order of convergence, obtaining new efficient high-order methods. We use the classical efficiency index to compare the obtained procedures and make some numerical test, that allow us to confirm the theoretical results.