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International Journal of Differential Equations
Volume 2014 (2014), Article ID 495357, 6 pages
http://dx.doi.org/10.1155/2014/495357
Research Article

On Some Iterative Methods with Memory and High Efficiency Index for Solving Nonlinear Equations

Faculty of Mathematics, University of Sistan and Baluchestan, Zahedan 987-98155, Iran

Received 25 December 2013; Accepted 10 March 2014; Published 6 April 2014

Academic Editor: Fawang Liu

Copyright © 2014 Tahereh Eftekhari. 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.

Linked References

  1. J. F. Traub, Iterative Methods for the Solution of Equations, Prentice-Hall, New Jersey, NJ, USA, 1964. View at MathSciNet
  2. J. F. Steffensen, “Remarks on iteration,” Skandinavisk Aktuarietidskrift, vol. 16, pp. 64–72, 1933.
  3. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. F. Soleymani and S. Shateyi, “Some iterative methods free from derivatives and their basins of attraction for nonlinear equations,” Discrete Dynamics in Nature and Society, vol. 2013, Article ID 301718, 10 pages, 2013. View at Publisher · View at Google Scholar
  5. 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, Article ID 568740, 15 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. F. Soleymani, “Some optimal iterative methods and their with memory variants,” Journal of the Egyptian Mathematical Society, vol. 21, no. 2, pp. 133–141, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. F. Soleymani and V. Hosseinabadi, “New third- and sixth-order derivative-free techniques for nonlinear equations,” Journal of Mathematics Research, vol. 3, 2011.
  8. T. Eftekhari, “A new sixth-order Steffensen-type iterative method for solving nonlinear equations,” International Journal of Analysis, vol. 2014, Article ID 685796, 5 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  9. M. Dehghan and M. Hajarian, “Some derivative free quadratic and cubic convergence iterative formulas for solving nonlinear equations,” Computational & Applied Mathematics, vol. 29, no. 1, pp. 19–30, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. A. Cordero, J. L. Hueso, E. Martínez, and J. R. Torregrosa, “Steffensen type methods for solving nonlinear equations,” Journal of Computational and Applied Mathematics, vol. 236, no. 12, pp. 3058–3064, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. J. Džunić, M. S. Petković, and L. D. Petković, “Three-point methods with and without memory for solving nonlinear equations,” Applied Mathematics and Computation, vol. 218, no. 9, pp. 4917–4927, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. R. Thukral, “A family of three-point derivative-free methods of eighth-order for solving nonlinear equations,” Journal of Modern Methods in Numerical Mathematics, vol. 3, no. 2, pp. 11–21, 2012.
  13. J. R. Sharma, R. K. Guha, and P. Gupta, “Some efficient derivative free methods with memory for solving nonlinear equations,” Applied Mathematics and Computation, vol. 219, no. 2, pp. 699–707, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  14. M. S. Petković, “Remarks on “On a general class of multipoint root-finding methods of high computational efficiency”,” SIAM Journal on Numerical Analysis, vol. 49, no. 3, pp. 1317–1319, 2011. View at Publisher · View at Google Scholar · View at MathSciNet