Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 198943, 12 pages
doi:10.1155/2010/198943
Research Article

Some New Iterative Methods for Nonlinear Equations

Muhammad Aslam Noor,1,2 Khalida Inayat Noor,1 Eisa Al-Said,2 and Muhammad Waseem1

1Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Islamabad 44000, Pakistan
2Mathematics Department, College of Science, King Saud University, Riyadh 11451, Saudi Arabia

Received 1 October 2010; Accepted 20 December 2010

Academic Editor: Carlo Cattani

Copyright © 2010 Muhammad Aslam Noor 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

We suggest and analyze some new iterative methods for solving the nonlinear equations 𝑓 ( 𝑥 ) = 0 using the decomposition technique coupled with the system of equations. We prove that new methods have convergence of fourth order. Several numerical examples are given to illustrate the efficiency and performance of the new methods. Comparison with other similar methods is given.