Solving a Nonlinear Equation Using a New Two-Step Derivative Free Iterative Methods

Alyauma Hajjah

doi:doi:10.11648/j.acm.20170606.11

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Solving a Nonlinear Equation Using a New Two-Step Derivative Free Iterative Methods

Alyauma Hajjah

Published in Applied and Computational Mathematics (Volume 6, Issue 6)

Received: 8 August 2017 Accepted: 26 September 2017 Published: 7 November 2017

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Abstract

In this paper, suggest anew two step iterative method for solving a nonlinear equation, which is derivative free by approximating a derivative in the iterative method by central difference with one parameter θ. The anew derivative free iterative method has a convergence of order four and computational cost the family requires three evaluations of functions per iteration. Numerical experiments show that the proposed a method is comparable to the existing method in terms of the number of iterations.

Published in	Applied and Computational Mathematics (Volume 6, Issue 6)
DOI	10.11648/j.acm.20170606.11
Page(s)	238-242
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), 2017. Published by Science Publishing Group

Keywords

Nonlinear Equation, Iterative Method, Derivative Free, Central Difference, Convergence of Order

References

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[3]	W. Bi, H. Ren, and Q. Wu (2009). Three-step Iterative Methods with Eight-order Convergence for Solving Nonlinear Equations, Journal of Computation and Applied Mathmatics, 225, 105-112.
[4]	A. Cordero, J. L. Hueso, E. Martinez, and J. R. Torregrosa, 2011. Steffensen type methods for solving nonlinear equations, Journal of Computational and Applied Mathematics, doi: 10.1016/j.cam. 2010.08.043.
[5]	M. Dehghan and M. Hajarian. Some Derivative Free Quadratic and Cubic Convergence Iterative Formulas for Solving Nonlinear Equation, J. Comput. Appl. Math, 29 (2010), 19-31.
[6]	W. Gautschi, Numerical Analysis: an Introduction, Birkhauser, 1997.
[7]	A. Hajjah, M. Imran and M. D. H. Gamal. A Two-Step Iterative Methods for Solving Nonlinear Equation, J. Applied Mathematics Sciences, Vol.8, 2014, No.161, 8021-8027.
[8]	M. Imran, Agusni, A. Karma, S. Putra. Two Step Methods Without Employing Derivatives for Solving a Nonlinear Equation, Bulletin of Mathematics. Vol.04, 2012, No.01, 59-65.
[9]	R. Intan, M. Imran, and M. D. H. Gamal. A Three-step Derivative Free Iterative Method for Solving a Nonlinear Equation, J. Applied Mathematics Scinces, Vol. 8, 2014, No. 89, 4425 – 4431.
[10]	J. P. Jaiswal. A New Third-Order Derivative Free Method for Solving Equations, Univ. J. Appl. Math. Comput, 184 (2006), 471-475.
[11]	K. Jisheng, L. Yetian and W. Xiuhui. A Composite Fourth-Order Iterative Method for Solving, Appl. Math. 1 (2013), 131-135.
[12]	R. F. King. A Family of Fourth Order Methods for Nonlinear Equations, SIAM J. Numer. Anal. 10 (1973), 876-879.
[13]	J. H. Mathews. Numerical Method for Mathematical Science and Engineer, Prentice-Hall International, Upper Saddle River, NJ, 1987.
[14]	D. Nerinckx and D. Haegenans. A Comparison of Non-linear Equation Solver, J. Comput. Appl. Math. 2 (1976), 145148.
[15]	J. R. Rice. A set of 74 test functions non-linear equation solvers, Report Purdue University CSD TR 34 (1969).
[16]	R. Wait. The Numerical Solution of Algebraic Equation, Jhon Wiley and Sons, New York, 1979.
[17]	S. Weerakon, T. G. I. Fernando, A variant of Newton’s method with accelerated third-order convergence. Appl. Math. Lett. 13(2000) 87-93.

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Alyauma Hajjah. (2017). Solving a Nonlinear Equation Using a New Two-Step Derivative Free Iterative Methods. Applied and Computational Mathematics, 6(6), 238-242. https://doi.org/10.11648/j.acm.20170606.11

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ACS Style

Alyauma Hajjah. Solving a Nonlinear Equation Using a New Two-Step Derivative Free Iterative Methods. Appl. Comput. Math. 2017, 6(6), 238-242. doi: 10.11648/j.acm.20170606.11

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AMA Style

Alyauma Hajjah. Solving a Nonlinear Equation Using a New Two-Step Derivative Free Iterative Methods. Appl Comput Math. 2017;6(6):238-242. doi: 10.11648/j.acm.20170606.11

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@article{10.11648/j.acm.20170606.11,
  author = {Alyauma Hajjah},
  title = {Solving a Nonlinear Equation Using a New Two-Step Derivative Free Iterative Methods},
  journal = {Applied and Computational Mathematics},
  volume = {6},
  number = {6},
  pages = {238-242},
  doi = {10.11648/j.acm.20170606.11},
  url = {https://doi.org/10.11648/j.acm.20170606.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20170606.11},
  abstract = {In this paper, suggest anew two step iterative method for solving a nonlinear equation, which is derivative free by approximating a derivative in the iterative method by central difference with one parameter θ. The anew derivative free iterative method has a convergence of order four and computational cost the family requires three evaluations of functions per iteration. Numerical experiments show that the proposed a method is comparable to the existing method in terms of the number of iterations.},
 year = {2017}
}

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TY  - JOUR
T1  - Solving a Nonlinear Equation Using a New Two-Step Derivative Free Iterative Methods
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AB  - In this paper, suggest anew two step iterative method for solving a nonlinear equation, which is derivative free by approximating a derivative in the iterative method by central difference with one parameter θ. The anew derivative free iterative method has a convergence of order four and computational cost the family requires three evaluations of functions per iteration. Numerical experiments show that the proposed a method is comparable to the existing method in terms of the number of iterations.
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Author Information

Alyauma Hajjah

Department of Informatics Technical, (Sekolah Tinggi Ilmu Komputer) STIKOM Pelita Indonesia, Pekanbaru, Indonesia

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Alyauma Hajjah. (2017). Solving a Nonlinear Equation Using a New Two-Step Derivative Free Iterative Methods. Applied and Computational Mathematics, 6(6), 238-242. https://doi.org/10.11648/j.acm.20170606.11

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ACS Style

Alyauma Hajjah. Solving a Nonlinear Equation Using a New Two-Step Derivative Free Iterative Methods. Appl. Comput. Math. 2017, 6(6), 238-242. doi: 10.11648/j.acm.20170606.11

Copy | Download

AMA Style

Alyauma Hajjah. Solving a Nonlinear Equation Using a New Two-Step Derivative Free Iterative Methods. Appl Comput Math. 2017;6(6):238-242. doi: 10.11648/j.acm.20170606.11

Copy | Download

@article{10.11648/j.acm.20170606.11,
  author = {Alyauma Hajjah},
  title = {Solving a Nonlinear Equation Using a New Two-Step Derivative Free Iterative Methods},
  journal = {Applied and Computational Mathematics},
  volume = {6},
  number = {6},
  pages = {238-242},
  doi = {10.11648/j.acm.20170606.11},
  url = {https://doi.org/10.11648/j.acm.20170606.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20170606.11},
  abstract = {In this paper, suggest anew two step iterative method for solving a nonlinear equation, which is derivative free by approximating a derivative in the iterative method by central difference with one parameter θ. The anew derivative free iterative method has a convergence of order four and computational cost the family requires three evaluations of functions per iteration. Numerical experiments show that the proposed a method is comparable to the existing method in terms of the number of iterations.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Solving a Nonlinear Equation Using a New Two-Step Derivative Free Iterative Methods
AU  - Alyauma Hajjah
Y1  - 2017/11/07
PY  - 2017
N1  - https://doi.org/10.11648/j.acm.20170606.11
DO  - 10.11648/j.acm.20170606.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 238
EP  - 242
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20170606.11
AB  - In this paper, suggest anew two step iterative method for solving a nonlinear equation, which is derivative free by approximating a derivative in the iterative method by central difference with one parameter θ. The anew derivative free iterative method has a convergence of order four and computational cost the family requires three evaluations of functions per iteration. Numerical experiments show that the proposed a method is comparable to the existing method in terms of the number of iterations.
VL  - 6
IS  - 6
ER  -

Copy | Download