Journal of Applied Mathematics
Volume 2012 (2012), Article ID 927450, 13 pages
Research Article

Some New Variants of Cauchy's Methods for Solving Nonlinear Equations

1Fundamental Department, Aviation University of Air Force, Changchun 130022, China
2College of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450011, China

Received 25 July 2012; Revised 26 September 2012; Accepted 26 September 2012

Academic Editor: Changbum Chun

Copyright © 2012 Tianbao Liu and Hengyan Li. 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 and analyze some variants of Cauchy's methods free from second derivative for obtaining simple roots of nonlinear equations. The convergence analysis of the methods is discussed. It is established that the methods have convergence order three. Per iteration the new methods require two function and one first derivative evaluations. Numerical examples show that the new methods are comparable with the well-known existing methods and give better numerical results in many aspects.