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A Novel Iteration Class for Solution of Nonlinear Equation

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), 2014. 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.
Cite This Article
  • 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

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

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