- 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
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 301718, 10 pages
Some Iterative Methods Free from Derivatives and Their Basins of Attraction for Nonlinear Equations
1Department of Chemistry, Roudehen Branch, Islamic Azad University, Roudehen, Iran
2Department of Mathematics, Zahedan Branch, Islamic Azad University, Zahedan, Iran
3Department of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda, P. Bag X5050, Thohoyandou 0950, South Africa
Received 4 January 2013; Accepted 2 April 2013
Academic Editor: Fathi Allan
Copyright © 2013 Farahnaz Soleimani 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.
- A. Cordero, J. L. Hueso, E. Martínez, and J. R. Torregrosa, “A family of derivative-free methods with high order of convergence and its application to nonsmooth equations,” Abstract and Applied Analysis, vol. 2012, Article ID 836901, 15 pages, 2012.
- F. Soleymani and S. Shateyi, “Two optimal eighth-order derivative-free classes of iterative methods,” Abstract and Applied Analysis, vol. 2012, Article ID 318165, 14 pages, 2012.
- A. Iliev and N. Kyurkchiev, Methods in Numerical Analysis: Selected Topics in Numerical Analysis, LAP LAMBERT Academic Publishing, 2010.
- A. T. Tiruneh, W. N. Ndlela, and S. J. Nkambule, “A three point formula for finding roots of equations by the method of least squares,” Journal of Applied Mathematics and Bioinformatics, vol. 2, pp. 213–233, 2012.
- B. H. Dayton, T.-Y. Li, and Z. Zeng, “Multiple zeros of nonlinear systems,” Mathematics of Computation, vol. 80, no. 276, pp. 2143–2168, 2011.
- J. F. Traub, Iterative Methods for the Solution of Equations, Chelsea Publishing, London, UK, 2nd edition, 1982.
- H. T. Kung and J. F. Traub, “Optimal order of one-point and multipoint iteration,” Journal of the Association for Computing Machinery, vol. 21, pp. 643–651, 1974.
- F. Soleymani, S. K. Vanani, and A. Afghani, “A general three-step class of optimal iterations for nonlinear equations,” Mathematical Problems in Engineering, vol. 2011, Article ID 469512, 10 pages, 2011.
- F. Soleymani, “Optimized Steffensen-type methods with eighth-order convergence and high efficiency index,” International Journal of Mathematics and Mathematical Sciences, vol. 2012, Article ID 932420, 18 pages, 2012.
- P. Jain, “Steffensen type methods for solving non-linear equations,” Applied Mathematics and Computation, vol. 194, no. 2, pp. 527–533, 2007.
- S. Wagon, Mathematica in Action, Springer, Berlin, Germany, 3rd edition, 2010.
- F. Soleymani, “An efficient twelfth-order iterative method for finding all the solutions of nonlinear equations,” Journal of Computational Methods in Sciences and Engineering, 2012.
- S. K. Rahimian, F. Jalali, J. D. Seader, and R. E. White, “A new homotopy for seeking all real roots of a nonlinear equation,” Computers and Chemical Engineering, vol. 35, no. 3, pp. 403–411, 2011.
- A. Cayley, “The Newton-Fourier imaginary problem,” American Journal of Mathematics, vol. 2, article 97, 1879.
- M. Trott, The Mathematica Guidebook for Numerics, Springer, New York, NY, USA, 2006.
- M. L. Sahari and I. Djellit, “Fractal Newton basins,” Discrete Dynamics in Nature and Society, vol. 2006, Article ID 28756, 16 pages, 2006.
- J. L. Varona, “Graphic and numerical comparison between iterative methods,” The Mathematical Intelligencer, vol. 24, no. 1, pp. 37–46, 2002.
- F. Chicharro, A. Cordero, J. M. Gutiérrez, and J. R. Torregrosa, “Complex dynamics of derivative-free methods for nonlinear equations,” Applied Mathematics and Computation, vol. 219, no. 12, pp. 7023–7035, 2013.
- J. M. Gutiérrez, M. A. Hernández, and N. Romero, “Dynamics of a new family of iterative processes for quadratic polynomials,” Journal of Computational and Applied Mathematics, vol. 233, no. 10, pp. 2688–2695, 2010.
- S. Artidiello, F. Chicharro, A. Cordero, and J. R. Torregrosa, “Local convergence and dynamical analysis of a new family of optimal fourth-order iterative methods,” International Journal of Computer Mathematics, 2013.