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

Noori Yasir Abdul-Hassan

doi:doi:10.11648/j.ajam.20160404.12

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

Noori Yasir Abdul-Hassan

Published in American Journal of Applied Mathematics (Volume 4, Issue 4)

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), 2024. Published by Science Publishing Group

Keywords

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

References

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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

Noori Yasir Abdul-Hassan

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

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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}
}

Copy | Download

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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