- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 720640, 2 pages
Comment on “A New Second-Order Iteration Method for Solving Nonlinear Equations”
School of Mechanical, College of Science, Inner Mongolia University of Technology, Hohhot 010051, China
Received 21 May 2013; Accepted 1 September 2013
Academic Editor: Allan Peterson
Copyright © 2013 Haibin 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.
Kang et al. claimed that they obtained a new iteration formulation for nonlinear algebraic equations; however the “new” formulation was first derived in 2007 by the variational iteration method.
Recently Kang et al. studied the following algebraic equation: and obtained the following iteration formulation [1, Equation ]:
Consider a nonlinear algebraic equation
Using the basic idea of the variational iteration method as illustrated in  (see in ), we can construct an iteration formulation for (1) in the form where is a Lagrange multiplier. To identify the multiplier, we set (see [2, Equation ]) from which the multiplier can be identified, which is This results in
Remark 4. The derivation process is the same as that given in .
- S. M. Kang, A. Rafiq, and Y. C. Kwun, “A new second-order iteration method for solving nonlinear equations,” Abstract and Applied Analysis, vol. 2013, Article ID 487062, 4 pages, 2013.
- J. H. He, “Variational iteration method-Some recent results and new interpretations,” Journal of Computational and Applied Mathematics, vol. 207, no. 1, pp. 3–17, 2007.
- J.-H. He, Y.-Q. Wan, and Q. Guo, “An iteration formulation for normalized diode characteristics,” International Journal of Circuit Theory and Applications, vol. 32, no. 6, pp. 629–632, 2004.
- J.-H. He, “A new iteration method for solving algebraic equations,” Applied Mathematics and Computation, vol. 135, no. 1, pp. 81–84, 2003.
- X.-G. Luo, “A note on the new iteration method for solving algebraic equations,” Applied Mathematics and Computation, vol. 171, no. 2, pp. 1177–1183, 2005.
- J.-H. He, “Some asymptotic methods for strongly nonlinear equations,” International Journal of Modern Physics B, vol. 20, no. 10, pp. 1141–1199, 2006.
- J. H. He, “Asymptotic methods for solitary solutions and compactons,” Abstract and Applied Analysis, vol. 2012, Article ID 916793, 130 pages, 2012.