A Novel Iteration Class for Solution of Nonlinear Equation

Hamideh Eskandari

doi:doi:10.11648/j.ajam.20140205.16

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A Novel Iteration Class for Solution of Nonlinear Equation

Hamideh Eskandari

Published in American Journal of Applied Mathematics (Volume 2, Issue 5)

Received: 3 October 2014 Accepted: 16 October 2014 Published: 30 October 2014

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Abstract

In this paper, one of the most fundament problems in numerical analysis has designed that it is found roots of equation f(x)=0 with variable x. In different articles and books, many several of methods exist for solving non algebra equations. Here, we present a class of Halley method and Chebyshev method from second derivatives for solving non algebra equations. In fact, it can be said that the best and the most convenient solution is the Newton method. We have this new method called class of Halley-Chebyshev method that this method also has second derivatives.

Published in	American Journal of Applied Mathematics (Volume 2, Issue 5)
DOI	10.11648/j.ajam.20140205.16
Page(s)	186-190
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

Non Algebra Equation, Newton Method, Hybrid Method, Halley Method, Chebyshev Method

References

[1]	Jisheng Kou, Yitian Li, Xiuhua Wang, On modified Newton methods with cubic convergence, Applied Mathematics and Computation, 176 (2006) 123–127.
[2]	Jisheng Kou, Yitian Li, Xiuhua Wang, A uniparametric Chebyshev-type method free from second derivatives, Applied Mathematics and Computation, 179 (2006) 296–300.
[3]	Nasr-Al-Din Ide, A new hybrid iteration method for algebraic equations, Applied Mathematics and Computation, 195 (2008) 772-774.
[4]	Hamideh Eskandari, A new numerical solving method for equations of one variable, International Journal of Applied Mathematics and Computer Sciences, 5:3 (2009) 183-186.
[5]	Stoer .J, Bulirsch .R, Introduction to numerical analysis, Springer-Verlag, 3rd ed., 2002.
[6]	Hildebrand .F.B, Introduction to numerical analysis, Tata McGraw-Hill, Second edition, 1987.
[7]	Fang .T, Fang .G, Lee .C.F, A new iteration method with cubic convergence to solve nonlinear algebraic equations, Applied Mathematics and Computation, 175 (2006) 1147-1155.
[8]	Atkinson, Kendall E. An introduction to numerical analysis, John Wiley & Sons, 1988.

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APA Style

Hamideh Eskandari. (2014). A Novel Iteration Class for Solution of Nonlinear Equation. American Journal of Applied Mathematics, 2(5), 186-190. https://doi.org/10.11648/j.ajam.20140205.16

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Hamideh Eskandari. A Novel Iteration Class for Solution of Nonlinear Equation. Am. J. Appl. Math. 2014, 2(5), 186-190. doi: 10.11648/j.ajam.20140205.16

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AMA Style

Hamideh Eskandari. A Novel Iteration Class for Solution of Nonlinear Equation. Am J Appl Math. 2014;2(5):186-190. doi: 10.11648/j.ajam.20140205.16

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@article{10.11648/j.ajam.20140205.16,
  author = {Hamideh Eskandari},
  title = {A Novel Iteration Class for Solution of Nonlinear Equation},
  journal = {American Journal of Applied Mathematics},
  volume = {2},
  number = {5},
  pages = {186-190},
  doi = {10.11648/j.ajam.20140205.16},
  url = {https://doi.org/10.11648/j.ajam.20140205.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20140205.16},
  abstract = {In this paper, one of the most fundament problems in numerical analysis has designed that it is found roots of equation f(x)=0 with variable x. In different articles and books, many several of methods exist for solving non algebra equations. Here, we present a class of Halley method and Chebyshev method from second derivatives for solving non algebra equations. In fact, it can be said that the best and the most convenient solution is the Newton method. We have this new method called class of Halley-Chebyshev method that this method also has second derivatives.},
 year = {2014}
}

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TY  - JOUR
T1  - A Novel Iteration Class for Solution of Nonlinear Equation
AU  - Hamideh Eskandari
Y1  - 2014/10/30
PY  - 2014
N1  - https://doi.org/10.11648/j.ajam.20140205.16
DO  - 10.11648/j.ajam.20140205.16
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 186
EP  - 190
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20140205.16
AB  - In this paper, one of the most fundament problems in numerical analysis has designed that it is found roots of equation f(x)=0 with variable x. In different articles and books, many several of methods exist for solving non algebra equations. Here, we present a class of Halley method and Chebyshev method from second derivatives for solving non algebra equations. In fact, it can be said that the best and the most convenient solution is the Newton method. We have this new method called class of Halley-Chebyshev method that this method also has second derivatives.
VL  - 2
IS  - 5
ER  -

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Author Information

Hamideh Eskandari

Department of Mathematics, Payame Noor University, Isfahan, I. R. Iran

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Plain Text BibTeX RIS

APA Style

Hamideh Eskandari. (2014). A Novel Iteration Class for Solution of Nonlinear Equation. American Journal of Applied Mathematics, 2(5), 186-190. https://doi.org/10.11648/j.ajam.20140205.16

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ACS Style

Hamideh Eskandari. A Novel Iteration Class for Solution of Nonlinear Equation. Am. J. Appl. Math. 2014, 2(5), 186-190. doi: 10.11648/j.ajam.20140205.16

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AMA Style

Hamideh Eskandari. A Novel Iteration Class for Solution of Nonlinear Equation. Am J Appl Math. 2014;2(5):186-190. doi: 10.11648/j.ajam.20140205.16

Copy | Download

@article{10.11648/j.ajam.20140205.16,
  author = {Hamideh Eskandari},
  title = {A Novel Iteration Class for Solution of Nonlinear Equation},
  journal = {American Journal of Applied Mathematics},
  volume = {2},
  number = {5},
  pages = {186-190},
  doi = {10.11648/j.ajam.20140205.16},
  url = {https://doi.org/10.11648/j.ajam.20140205.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20140205.16},
  abstract = {In this paper, one of the most fundament problems in numerical analysis has designed that it is found roots of equation f(x)=0 with variable x. In different articles and books, many several of methods exist for solving non algebra equations. Here, we present a class of Halley method and Chebyshev method from second derivatives for solving non algebra equations. In fact, it can be said that the best and the most convenient solution is the Newton method. We have this new method called class of Halley-Chebyshev method that this method also has second derivatives.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - A Novel Iteration Class for Solution of Nonlinear Equation
AU  - Hamideh Eskandari
Y1  - 2014/10/30
PY  - 2014
N1  - https://doi.org/10.11648/j.ajam.20140205.16
DO  - 10.11648/j.ajam.20140205.16
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 186
EP  - 190
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20140205.16
AB  - In this paper, one of the most fundament problems in numerical analysis has designed that it is found roots of equation f(x)=0 with variable x. In different articles and books, many several of methods exist for solving non algebra equations. Here, we present a class of Halley method and Chebyshev method from second derivatives for solving non algebra equations. In fact, it can be said that the best and the most convenient solution is the Newton method. We have this new method called class of Halley-Chebyshev method that this method also has second derivatives.
VL  - 2
IS  - 5
ER  -

Copy | Download