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New Predictor-Corrector Iterative Methods with Twelfth-Order Convergence for Solving Nonlinear Equations

Received: 16 May 2016     Accepted: 31 May 2016     Published: 17 June 2016
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Abstract

In this paper, we propose and analyze new two efficient iterative methods for finding the simple roots of nonlinear equations. These methods based on a Jarratt's method, Householder's method and Chun&Kim's method by using a predictor-corrector technique. The error equations are given theoretically to show that the proposed methods have twelfth-order convergence. Several numerical examples are given to illustrate the efficiency and robustness of the proposed methods. Comparison with other well-known iterative methods is made.

Published in American Journal of Applied Mathematics (Volume 4, Issue 4)
DOI 10.11648/j.ajam.20160404.12
Page(s) 175-180
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Nonlinear Equations, Predictor-Corrector Methods, Convergence Analysis, Efficiency Index, Numerical Examples

References
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Cite This Article
  • APA Style

    Noori Yasir Abdul-Hassan. (2016). New Predictor-Corrector Iterative Methods with Twelfth-Order Convergence for Solving Nonlinear Equations. American Journal of Applied Mathematics, 4(4), 175-180. https://doi.org/10.11648/j.ajam.20160404.12

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    ACS Style

    Noori Yasir Abdul-Hassan. New Predictor-Corrector Iterative Methods with Twelfth-Order Convergence for Solving Nonlinear Equations. Am. J. Appl. Math. 2016, 4(4), 175-180. doi: 10.11648/j.ajam.20160404.12

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    AMA Style

    Noori Yasir Abdul-Hassan. New Predictor-Corrector Iterative Methods with Twelfth-Order Convergence for Solving Nonlinear Equations. Am J Appl Math. 2016;4(4):175-180. doi: 10.11648/j.ajam.20160404.12

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  • @article{10.11648/j.ajam.20160404.12,
      author = {Noori Yasir Abdul-Hassan},
      title = {New Predictor-Corrector Iterative Methods with Twelfth-Order Convergence for Solving Nonlinear Equations},
      journal = {American Journal of Applied Mathematics},
      volume = {4},
      number = {4},
      pages = {175-180},
      doi = {10.11648/j.ajam.20160404.12},
      url = {https://doi.org/10.11648/j.ajam.20160404.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20160404.12},
      abstract = {In this paper, we propose and analyze new two efficient iterative methods for finding the simple roots of nonlinear equations. These methods based on a Jarratt's method, Householder's method and Chun&Kim's method by using a predictor-corrector technique. The error equations are given theoretically to show that the proposed methods have twelfth-order convergence. Several numerical examples are given to illustrate the efficiency and robustness of the proposed methods. Comparison with other well-known iterative methods is made.},
     year = {2016}
    }
    

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  • TY  - JOUR
    T1  - New Predictor-Corrector Iterative Methods with Twelfth-Order Convergence for Solving Nonlinear Equations
    AU  - Noori Yasir Abdul-Hassan
    Y1  - 2016/06/17
    PY  - 2016
    N1  - https://doi.org/10.11648/j.ajam.20160404.12
    DO  - 10.11648/j.ajam.20160404.12
    T2  - American Journal of Applied Mathematics
    JF  - American Journal of Applied Mathematics
    JO  - American Journal of Applied Mathematics
    SP  - 175
    EP  - 180
    PB  - Science Publishing Group
    SN  - 2330-006X
    UR  - https://doi.org/10.11648/j.ajam.20160404.12
    AB  - In this paper, we propose and analyze new two efficient iterative methods for finding the simple roots of nonlinear equations. These methods based on a Jarratt's method, Householder's method and Chun&Kim's method by using a predictor-corrector technique. The error equations are given theoretically to show that the proposed methods have twelfth-order convergence. Several numerical examples are given to illustrate the efficiency and robustness of the proposed methods. Comparison with other well-known iterative methods is made.
    VL  - 4
    IS  - 4
    ER  - 

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Author Information
  • Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah, Iraq

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