Combination of Newton-Halley-Chebyshev Iterative Methods Without Second Derivatives

Ahmad Syakir; M. Imran; Moh Danil Hendry Gamal

doi:doi:10.11648/j.ijtam.20170303.12

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Combination of Newton-Halley-Chebyshev Iterative Methods Without Second Derivatives

Ahmad Syakir, M. Imran, Moh Danil Hendry Gamal

Published in International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 3)

Received: 11 April 2017 Accepted: 21 April 2017 Published: 19 May 2017

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Abstract

This article discusses the modification of three step iteration method to solve nonlinear equations f (x)=0. The new iterative method is formed from a combination of Newton, Halley, and Chebyshev methods. To reduce the number of evaluation functions, some derivatives in this method are estimated by Taylor polynomials. Using analysis of convergence we show that the new method has the order of convergence fourteen. Numerical computation shows that the new method are comparable to other methods discussed.

Published in	International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 3)
DOI	10.11648/j.ijtam.20170303.12
Page(s)	106-109
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

Free Second Derivative Method, Taylor Series, Iterative Method, Order of Convergence

References

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[2]	M. S. M. Bahgat and M. A. Hafiz, Three step iterative method with eighteenth order convergence for solving nonlinear equations, International Journal of Pure and Applied Mathematics, 93 (2014), 85-94.
[3]	R. Behl and V. Kanwar, Variant of Chebyshev's methods with optimal order convergence, Tamsui Oxford Journal of Information and Mathematical Sciences, 29 (2013), 39-53.
[4]	M. A. Hafiz, An efficient three step tenth order method without second order derivative, Palestine Journal of Mathematics, 3 (2014), 198-203.
[5]	M. A. Hafiz and S. M. H. Al-Goria, New ninth and seventh order methods for solving nonlinear equations, Europian Scientific Journal, 8 (2012), 83-95.
[6]	R. King, A family of fourth order methods for nonlinear equations, Journal of Numerical Analysis, 10 (1973), 876-879.
[7]	J. Kou, Y. Li, and X. Wang, Modified Halley's method free from second derivative, Applied Mathematics and Computation, 183 (2006), 704-708.
[8]	J. H. Mathews and K. D. Fink, Numerical Methods Using MATLAB, third Ed., Prentice Hall, New Jersey, 1999.
[9]	M. Matinfar, M. Aminzadeh, and S. Asadpour, A new three step iterative method for solving nonlinear equations, Journal of Mathematical Extension, 6 (2012), 29-39.
[10]	K. I. Noor and M. A. Noor, Predictor-corrector Halley method for nonlinear equations, Applied Mathematics and Computation, 188 (2007), 1587-1591.
[11]	M. A. Noor, W. A. Khan, and A. Hussain, A new modified Halley method without second derivatives for nonlinear equations, Applied Mathematics and Computation, 189 (2007), 1268-1273.
[12]	M. Rafiullah and M. Haleem, Three step iterative method with sixth order convergence for solving nonlinear equations, International Journal of Mathematic Analysis, 50 (2010), 2459-2463.
[13]	G. Zavalani, A modification of Newton method with third order convergence, American Journal of Numerical Analysis, 2 (2014), 98-101.

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APA Style

Ahmad Syakir, M. Imran, Moh Danil Hendry Gamal. (2017). Combination of Newton-Halley-Chebyshev Iterative Methods Without Second Derivatives. International Journal of Theoretical and Applied Mathematics, 3(3), 106-109. https://doi.org/10.11648/j.ijtam.20170303.12

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ACS Style

Ahmad Syakir; M. Imran; Moh Danil Hendry Gamal. Combination of Newton-Halley-Chebyshev Iterative Methods Without Second Derivatives. Int. J. Theor. Appl. Math. 2017, 3(3), 106-109. doi: 10.11648/j.ijtam.20170303.12

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AMA Style

Ahmad Syakir, M. Imran, Moh Danil Hendry Gamal. Combination of Newton-Halley-Chebyshev Iterative Methods Without Second Derivatives. Int J Theor Appl Math. 2017;3(3):106-109. doi: 10.11648/j.ijtam.20170303.12

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@article{10.11648/j.ijtam.20170303.12,
  author = {Ahmad Syakir and M. Imran and Moh Danil Hendry Gamal},
  title = {Combination of Newton-Halley-Chebyshev Iterative Methods Without Second Derivatives},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {3},
  number = {3},
  pages = {106-109},
  doi = {10.11648/j.ijtam.20170303.12},
  url = {https://doi.org/10.11648/j.ijtam.20170303.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20170303.12},
  abstract = {This article discusses the modification of three step iteration method to solve nonlinear equations f (x)=0. The new iterative method is formed from a combination of Newton, Halley, and Chebyshev methods. To reduce the number of evaluation functions, some derivatives in this method are estimated by Taylor polynomials. Using analysis of convergence we show that the new method has the order of convergence fourteen. Numerical computation shows that the new method are comparable to other methods discussed.},
 year = {2017}
}

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TY  - JOUR
T1  - Combination of Newton-Halley-Chebyshev Iterative Methods Without Second Derivatives
AU  - Ahmad Syakir
AU  - M. Imran
AU  - Moh Danil Hendry Gamal
Y1  - 2017/05/19
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N1  - https://doi.org/10.11648/j.ijtam.20170303.12
DO  - 10.11648/j.ijtam.20170303.12
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
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PB  - Science Publishing Group
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AB  - This article discusses the modification of three step iteration method to solve nonlinear equations f (x)=0. The new iterative method is formed from a combination of Newton, Halley, and Chebyshev methods. To reduce the number of evaluation functions, some derivatives in this method are estimated by Taylor polynomials. Using analysis of convergence we show that the new method has the order of convergence fourteen. Numerical computation shows that the new method are comparable to other methods discussed.
VL  - 3
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Author Information

Ahmad Syakir

Department of Mathematics, University of Riau, Pekanbaru, Indonesia
M. Imran

Department of Mathematics, University of Riau, Pekanbaru, Indonesia
Moh Danil Hendry Gamal

Department of Mathematics, University of Riau, Pekanbaru, Indonesia

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APA Style

Ahmad Syakir, M. Imran, Moh Danil Hendry Gamal. (2017). Combination of Newton-Halley-Chebyshev Iterative Methods Without Second Derivatives. International Journal of Theoretical and Applied Mathematics, 3(3), 106-109. https://doi.org/10.11648/j.ijtam.20170303.12

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ACS Style

Ahmad Syakir; M. Imran; Moh Danil Hendry Gamal. Combination of Newton-Halley-Chebyshev Iterative Methods Without Second Derivatives. Int. J. Theor. Appl. Math. 2017, 3(3), 106-109. doi: 10.11648/j.ijtam.20170303.12

Copy | Download

AMA Style

Ahmad Syakir, M. Imran, Moh Danil Hendry Gamal. Combination of Newton-Halley-Chebyshev Iterative Methods Without Second Derivatives. Int J Theor Appl Math. 2017;3(3):106-109. doi: 10.11648/j.ijtam.20170303.12

Copy | Download

@article{10.11648/j.ijtam.20170303.12,
  author = {Ahmad Syakir and M. Imran and Moh Danil Hendry Gamal},
  title = {Combination of Newton-Halley-Chebyshev Iterative Methods Without Second Derivatives},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {3},
  number = {3},
  pages = {106-109},
  doi = {10.11648/j.ijtam.20170303.12},
  url = {https://doi.org/10.11648/j.ijtam.20170303.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20170303.12},
  abstract = {This article discusses the modification of three step iteration method to solve nonlinear equations f (x)=0. The new iterative method is formed from a combination of Newton, Halley, and Chebyshev methods. To reduce the number of evaluation functions, some derivatives in this method are estimated by Taylor polynomials. Using analysis of convergence we show that the new method has the order of convergence fourteen. Numerical computation shows that the new method are comparable to other methods discussed.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Combination of Newton-Halley-Chebyshev Iterative Methods Without Second Derivatives
AU  - Ahmad Syakir
AU  - M. Imran
AU  - Moh Danil Hendry Gamal
Y1  - 2017/05/19
PY  - 2017
N1  - https://doi.org/10.11648/j.ijtam.20170303.12
DO  - 10.11648/j.ijtam.20170303.12
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 106
EP  - 109
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20170303.12
AB  - This article discusses the modification of three step iteration method to solve nonlinear equations f (x)=0. The new iterative method is formed from a combination of Newton, Halley, and Chebyshev methods. To reduce the number of evaluation functions, some derivatives in this method are estimated by Taylor polynomials. Using analysis of convergence we show that the new method has the order of convergence fourteen. Numerical computation shows that the new method are comparable to other methods discussed.
VL  - 3
IS  - 3
ER  -

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