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Discrete Dynamics in Nature and Society
Volume 2017 (2017), Article ID 3794357, 8 pages
https://doi.org/10.1155/2017/3794357
Research Article

Decomposition Technique and a Family of Efficient Schemes for Nonlinear Equations

1Department of Mathematics, COMSATS Institute of Information Technology, Attock Campus, Attock, Pakistan
2School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia
3Department of Mathematics, University of Education, Attock Campus, Attock, Pakistan

Correspondence should be addressed to Farooq Ahmed Shah

Received 25 April 2017; Accepted 17 August 2017; Published 1 October 2017

Academic Editor: Qamar Din

Copyright © 2017 Farooq Ahmed Shah 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. S. Abbasbandy, “Improving Newton-Raphson method for nonlinear equations by modified Adomian decomposition method,” Applied Mathematics and Computation, vol. 145, no. 2-3, pp. 887–893, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. S. Bhalekar and V. Daftardar-Gejji, “Convergence of the new iterative method,” International Journal of Differential Equations, vol. 2011, Article ID 989065, 2011. View at Publisher · View at Google Scholar · View at Scopus
  3. G. Adomian, Nonlinear Stochastic Systems Theory and Applications to Physics, Kluwer Academic, Dordrecht, The Netherlands, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  4. C. Chun, H. j. Bae, and B. Neta, “New families of nonlinear third-order solvers for finding multiple roots,” Computers and Mathematics with Applications. An International Journal, vol. 57, no. 9, pp. 1574–1582, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  5. J.-H. He, “A new iteration method for solving algebraic equations,” Applied Mathematics and Computation, vol. 135, no. 1, pp. 81–84, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. K. I. Noor and M. A. Noor, “Predictor-corrector Halley method for nonlinear equations,” Applied Mathematics and Computation, vol. 188, no. 2, pp. 1587–1591, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  7. V. Daftardar-Gejji and H. Jafari, “An iterative method for solving nonlinear functional equations,” Journal of Mathematical Analysis and Applications, vol. 316, no. 2, pp. 753–763, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. M. A. Noor and K. I. Noor, “Some iterative schemes for nonlinear equations,” Applied Mathematics and Computation, vol. 183, no. 2, pp. 774–779, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  9. M. A. Noor, “New classes of iterative methods for nonlinear equations,” Applied Mathematics and Computation, vol. 191, no. 1, pp. 128–131, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  10. J. H. Yun, “A note on three-step iterative method for nonlinear equations,” Applied Mathematics and Computation, vol. 202, no. 1, pp. 401–405, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. F. A. Shah and M. A. Noor, “Higher order iterative schemes for nonlinear equations using decomposition technique,” Applied Mathematics and Computation, vol. 266, Article ID 21175, pp. 414–423, 2015. View at Publisher · View at Google Scholar · View at MathSciNet