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Complexity
Volume 2017 (2017), Article ID 6457532, 11 pages
https://doi.org/10.1155/2017/6457532
Research Article

Efficient High-Order Iterative Methods for Solving Nonlinear Systems and Their Application on Heat Conduction Problems

1Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Valencia, Spain
2Universitat de València, Valencia, Spain

Correspondence should be addressed to Alicia Cordero; se.vpu.tam@oredroca

Received 18 July 2016; Accepted 19 December 2016; Published 22 January 2017

Academic Editor: Sergio Gómez

Copyright © 2017 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

For solving nonlinear systems of big size, such as those obtained by applying finite differences for approximating the solution of diffusion problem and heat conduction equations, three-step iterative methods with eighth-order local convergence are presented. The computational efficiency of the new methods is compared with those of some known ones, obtaining good conclusions, due to the particular structure of the iterative expression of the proposed methods. Numerical comparisons are made with the same existing methods, on standard nonlinear systems and a nonlinear one-dimensional heat conduction equation by transforming it in a nonlinear system by using finite differences. From these numerical examples, we confirm the theoretical results and show the performance of the presented schemes.