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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 301718, 10 pages
http://dx.doi.org/10.1155/2013/301718
Research Article

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.

Citations to this Article [9 citations]

The following is the list of published articles that have cited the current article.

  • Fazlollah Soleymani, Stanford Shateyi, and Gülcan Özkum, “An Iterative Solver in the Presence and Absence of Multiplicity for Nonlinear Equations,” The Scientific World Journal, vol. 2013, pp. 1–9, 2013. View at Publisher · View at Google Scholar
  • Malik Zaka Ullah, A. S. Al-Fhaid, and Fayyaz Ahmad, “Four-Point Optimal Sixteenth-Order Iterative Method for Solving Nonlinear Equations,” Journal of Applied Mathematics, vol. 2013, pp. 1–5, 2013. View at Publisher · View at Google Scholar
  • Alicia Cordero, Fazlollah Soleymani, and Juan R. Torregrosa, “Dynamical analysis of iterative methods for nonlinear systems or how to deal with the dimension?,” Applied Mathematics and Computation, vol. 244, pp. 398–412, 2014. View at Publisher · View at Google Scholar
  • A. S. Al-Fhaid, S. Shateyi, M. Zaka Ullah, and F. Soleymani, “A Matrix Iteration for Finding Drazin Inverse with Ninth-Order Convergence,” Abstract and Applied Analysis, vol. 2014, pp. 1–7, 2014. View at Publisher · View at Google Scholar
  • Taher Lotfi, Alicia Cordero, Juan R. Torregrosa, Morteza Amir Abadi, and Maryam Mohammadi Zadeh, “On Generalization Based on Bi et al. Iterative Methods with Eighth-Order Convergence for Solving Nonlinear Equations,” The Scientific World Journal, vol. 2014, pp. 1–8, 2014. View at Publisher · View at Google Scholar
  • F. Soleymani, E. Tohidi, S. Shateyi, and F. Khaksar Haghani, “Some Matrix Iterations for Computing Matrix Sign Function,” Journal of Applied Mathematics, vol. 2014, pp. 1–9, 2014. View at Publisher · View at Google Scholar
  • Tahereh Eftekhari, “On Some Iterative Methods with Memory and High Efficiency Index for Solving Nonlinear Equations,” International Journal of Differential Equations, vol. 2014, pp. 1–6, 2014. View at Publisher · View at Google Scholar
  • Alicia Cordero, Fazlollah Soleymani, Juan R. Torregrosa, and Stanford Shateyi, “Basins of Attraction for Various Steffensen-Type Methods,” Journal of Applied Mathematics, vol. 2014, pp. 1–17, 2014. View at Publisher · View at Google Scholar
  • Taher Lotfi, and Elahe Tavakoli, “On a New Efficient Steffensen-Like Iterative Class by Applying a Suitable Self-Accelerator Parameter,” The Scientific World Journal, vol. 2014, pp. 1–9, 2014. View at Publisher · View at Google Scholar