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On novel classes of iterative methods for solving nonlinear equations

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Abstract

In this paper, we establish two new classes of derivative-involved methods for solving single valued nonlinear equations of the form f(x) = 0. The first contributed two-step class includes two evaluations of the function and one of its first derivative where its error analysis shows a fourth-order convergence. Next, we construct a three-step high-order class of methods including four evaluations per full cycle to achieve the seventh-order of convergence. Numerical examples are included to re-verify the theoretical results and moreover put on show the efficiency of the new methods from our classes.

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References

  1. T. Sauer, Numerical Analysis, Boston: Pearson, 2006.

    Google Scholar 

  2. M. A. Noor, K. I. Noor, E. Al-Said, and M. Waseem, “Some New Iterative Methods for Nonlinear Equations,” Math. Probl. Engng. vol. Article ID 198943 pages (2010).

  3. J. Kou, Y. Li, and X. Wang, “Some Variants of Ostrowski’s Method with Seventh-Order Convergence,” Comput. Appl. Math. 209, 153–159 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  4. A. Cordero, E. Hueso, E. Martínez, and J.R. Torregrosa, “Efficient Three-Step Iterative Methods with Sixth Order Convergence for Nonlinear Equations,” Numer. Algor. 53, 485–495 (2010).

    Article  MATH  Google Scholar 

  5. I. Pavaloiu, “Bilateral Approximations of Solutions of Equations by Order Three Steffensen-Type Methods,” Stud. Univ. Babes-Bolyai. Math. 51, 105–114 (2006).

    MathSciNet  MATH  Google Scholar 

  6. F. Soleymani, “Regarding the Accuracy of Optimal Eighth-Order Methods,” Math. Comput. Modelling 53, 1351–1357 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  7. F. Soleymani and M. Sharifi, “On a Class of Fifteenth-Order Iterative Formulas for Simple Roots,” Int. Electronic J. Pure Appl. Math. 3, 245–252 (2011).

    Google Scholar 

  8. Q. Ye and X. Xu, “Class of Newton-Like Methods with Cubic Convergence for Nonlinear Equations,” Fixed Point Theory 11, 161–168 (2010).

    MathSciNet  MATH  Google Scholar 

  9. J. F. Traub, Iterative Methods for Solution of Equations, New Jersey: Prentice-Hall, Englewood Cliffs, 1964.

    MATH  Google Scholar 

  10. H. T. Kung and J. F. Traub, “Optimal Order of One-Point and Multipoint Iteration,” J. ACM 643–651 (1974).

  11. R. King, “A Family of Fourth-Order Methods for Nonlinear Equations,” SIAM J. Numer. Analys. 10, 876–879 (1973).

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Islamic Azad University, Zahedan Branch, Zahedan, Iran

    Fazlollah Soleymani

  2. Young Researchers Club, Islamic Azad University, Zahedan Branch, Zahedan, Iran

    B. S. Mousavi

Authors
  1. Fazlollah Soleymani
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  2. B. S. Mousavi
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Correspondence to Fazlollah Soleymani.

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Soleymani, F., Mousavi, B.S. On novel classes of iterative methods for solving nonlinear equations. Comput. Math. and Math. Phys. 52, 203–210 (2012). https://doi.org/10.1134/S0965542512020133

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  • DOI: https://doi.org/10.1134/S0965542512020133

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