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Mathematical Problems in Engineering
Volume 2011, Article ID 469512, 10 pages
http://dx.doi.org/10.1155/2011/469512
Research Article

A General Three-Step Class of Optimal Iterations for Nonlinear Equations

1Young Researchers Club, Islamic Azad University, Zahedan Branch, Zahedan 98168, Iran
2Department of Mathematics, Islamic Azad University, Zahedan Branch, Zahedan 98168, Iran

Received 7 August 2011; Accepted 16 September 2011

Academic Editor: Hung Nguyen-Xuan

Copyright © 2011 Fazlollah Soleymani 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 [14 citations]

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

  • F. Soleymani, and S. Karimi Vanani, “Optimal Steffensen-type methods with eighth order of convergence,” Computers & Mathematics With Applications, vol. 62, no. 12, pp. 4619–4626, 2011. View at Publisher · View at Google Scholar
  • F. Soleymani, “Novel Computational Iterative Methods with Optimal Order for Nonlinear Equations,” Advances in Numerical Analysis, vol. 2011, pp. 1–10, 2011. View at Publisher · View at Google Scholar
  • Fazlollah Soleymani, S. Karimi Vanani, Hani I. Siyyam, and I. A. Al-Subaihi, “Numerical solution of nonlinear equations by an optimal eighth-order class of iterative methods,” Annali Dell'universita' Di Ferrara, vol. 59, no. 1, pp. 159–171, 2012. View at Publisher · View at Google Scholar
  • F. Soleymani, S. Karimi Vanani, M. Khan, and M. Sharifi, “Some modifications of King's family with optimal eighth order of convergence,” Mathematical And Computer Modelling, vol. 55, no. 3-4, pp. 1373–1380, 2012. View at Publisher · View at Google Scholar
  • F. Soleymani, S. Karimi Vanani, and M. Jamali Paghaleh, “A Class of Three-Step Derivative-Free Root Solvers with Optimal Convergence Order,” Journal of Applied Mathematics, vol. 2012, pp. 1–15, 2012. View at Publisher · View at Google Scholar
  • F. Soleymani, “Optimized Steffensen-Type Methods with Eighth-Order Convergence and High Efficiency Index,” International Journal of Mathematics and Mathematical Sciences, vol. 2012, pp. 1–18, 2012. View at Publisher · View at Google Scholar
  • Yanfang Wei, Qiang He, Yonghui Sun, Yanzhou Sun, and Cong Ji, “Improved Power Flow Algorithm for VSC-HVDC System Based on High-Order Newton-Type Method,” Mathematical Problems in Engineering, vol. 2013, pp. 1–10, 2013. View at Publisher · View at Google Scholar
  • Farahnaz Soleimani, Fazlollah Soleymani, and Stanford Shateyi, “Some Iterative Methods Free from Derivatives and Their Basins of Attraction for Nonlinear Equations,” Discrete Dynamics in Nature and Society, vol. 2013, pp. 1–10, 2013. View at Publisher · View at Google Scholar
  • Alicia Cordero, Taher Lotfi, Katayoun Mahdiani, and Juan R. Torregrosa, “Two Optimal General Classes of Iterative Methods with Eighth-Order,” Acta Applicandae Mathematicae, 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
  • Taher Lotfi, and Tahereh Eftekhari, “A New Optimal Eighth-Order Ostrowski-Type Family of Iterative Methods for Solving Nonlinear Equations,” Chinese Journal of Mathematics, vol. 2014, pp. 1–7, 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
  • 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
  • Nahid Zainali, and Taher Lotfi, “A globally convergent variant of mid-point method for finding the matrix sign,” Computational and Applied Mathematics, 2018. View at Publisher · View at Google Scholar