Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2012, Article ID 568740, 15 pages
http://dx.doi.org/10.1155/2012/568740
Research Article

A Class of Three-Step Derivative-Free Root Solvers with Optimal Convergence Order

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

Received 8 October 2011; Accepted 1 November 2011

Academic Editor: Yeong-Cheng Liou

Copyright © 2012 F. 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.

Linked References

  1. A. Iliev and N. Kyurkchiev, Nontrivial Methods in Numerical Analysis: Selected Topics in Numerical Analysis, LAP LAMBERT Academic Publishing, 2010. View at Zentralblatt MATH
  2. M. A. Hernández and N. Romero, “On the efficiency index of one-point iterative processes,” Numerical Algorithms, vol. 46, no. 1, pp. 35–44, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. F. Soleymani and M. Sharifi, “On a general efficient class of four-step root-finding methods,” International Journal of Mathematics and Computers in Simulation, vol. 5, pp. 181–189, 2011. View at Google Scholar
  4. F. Soleymani, “New optimal iterative methods in solving nonlinear equations,” International Journal of Pure and Applied Mathematics, vol. 72, no. 2, pp. 195–202, 2011. View at Google Scholar
  5. F. Soleymani, S. Karimi 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. View at Publisher · View at Google Scholar
  6. P. Sargolzaei and F. Soleymani, “Accurate fourteenth-order methods for solving nonlinear equations,” Numerical Algorithms, vol. 58, no. 4, pp. 513–527, 2011. View at Publisher · View at Google Scholar
  7. F. Soleymani, “A novel and precise sixth-order method for solving nonlinear equations,” International Journal of Mathematical Models and Methods in Applied Sciences, vol. 5, pp. 730–737, 2011. View at Google Scholar
  8. F. Soleymani, “On a bi-parametric class of optimal eighth-order derivative-free methods,” International Journal of Pure and Applied Mathematics, vol. 72, pp. 27–37, 2011. View at Google Scholar
  9. 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 Google Scholar · View at Zentralblatt MATH
  10. Y. Peng, H. Feng, Q. Li, and X. Zhang, “A fourth-order derivative-free algorithm for nonlinear equations,” Journal of Computational and Applied Mathematics, vol. 235, no. 8, pp. 2551–2559, 2011. View at Publisher · View at Google Scholar
  11. H. Ren, Q. Wu, and W. Bi, “A class of two-step Steffensen type methods with fourth-order convergence,” Applied Mathematics and Computation, vol. 209, no. 2, pp. 206–210, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. Z. Liu, Q. Zheng, and P. Zhao, “A variant of Steffensen's method of fourth-order convergence and its applications,” Applied Mathematics and Computation, vol. 216, no. 7, pp. 1978–1983, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. S. K. Khattri and I. K. Argyros, “Sixth order derivative free family of iterative methods,” Applied Mathematics and Computation, vol. 217, no. 12, pp. 5500–5507, 2011. View at Publisher · View at Google Scholar
  14. R. Thukral, “Eighth-order iterative methods without derivatives for solving nonlinear equations,” ISRN Applied Mathematics, vol. 2011, Article ID 693787, 12 pages, 2011. View at Publisher · View at Google Scholar
  15. F. Soleymani and V. Hosseinabadi, “New third- and sixth-order derivative-free techniques for nonlinear equations,” Journal of Mathematics Research, vol. 3, pp. 107–112, 2011. View at Google Scholar · View at Zentralblatt MATH
  16. F. Soleymani and S. Karimi Vanani, “Optimal Steffensen-type methods with eighth order of convergence,” Computers and Mathematics with Applications, vol. 62, no. 12, pp. 4619–4626, 2011. View at Publisher · View at Google Scholar
  17. F. Soleymani, “Two classes of iterative schemes for approximating simple roots,” Journal of Applied Sciences, vol. 11, no. 19, pp. 3442–3446, 2011. View at Publisher · View at Google Scholar
  18. F. Soleymani, “Regarding the accuracy of optimal eighth-order methods,” Mathematical and Computer Modelling, vol. 53, no. 5-6, pp. 1351–1357, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. F. Soleymani, S. K. Khattri, and S. Karimi Vanani, “Two new classes of optimal Jarratt-type fourth-order methods,” Applied Mathematics Letters, vol. 25, no. 5, pp. 847–853, 2012. View at Publisher · View at Google Scholar
  20. F. Soleymani, “Revisit of Jarratt method for solving nonlinear equations,” Numerical Algorithms, vol. 57, no. 3, pp. 377–388, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. D. K. R. Babajee, Analysis of higher order variants of Newton's method and their applications to differential and integral equations and in ocean acidification, Ph.D. thesis, University of Mauritius, 2010.
  22. F. Soleymani, “On a novel optimal quartically class of methods,” Far East Journal of Mathematical Sciences (FJMS), vol. 58, no. 2, pp. 199–206, 2011. View at Google Scholar
  23. 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
  24. F. Soleymani and B. S. Mousavi, “A novel computational technique for finding simple roots of nonlinear equations,” International Journal of Mathematical Analysis, vol. 5, pp. 1813–1819, 2011. View at Google Scholar
  25. F. Soleymani and M. Sharifi, “On a class of fifteenth-order iterative formulas for simple roots,” International Electronic Journal of Pure and Applied Mathematics, vol. 3, pp. 245–252, 2011. View at Google Scholar
  26. L. D. Petković, M. S. Petković, and J. Džunić, “A class of three-point root-solvers of optimal order of convergence,” Applied Mathematics and Computation, vol. 216, no. 2, pp. 671–676, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  27. X. Wang and L. Liu, “New eighth-order iterative methods for solving nonlinear equations,” Journal of Computational and Applied Mathematics, vol. 234, no. 5, pp. 1611–1620, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  28. B. I. Yun, “A non-iterative method for solving non-linear equations,” Applied Mathematics and Computation, vol. 198, no. 2, pp. 691–699, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  29. J. F. Traub, Iterative Methods for the Solution of Equations, Chelsea Publishing Company, New York, NY, USA, 1982.