| Peer-Reviewed

Generalized Difference Formula for a Nonlinear Equation

Received: 12 July 2014     Accepted: 22 July 2014     Published: 30 July 2014
Views:       Downloads:
Abstract

In this paper, a new iteration scheme is proposed to solve the roots of a nonlinear equation. It is the purpose of this paper to show that, although the new iteration method seems to be of high convergence, the results are promising in that it requires more computation work and even be divergent. In here, we use iteration method that applied derivatives of the first order and the second order; we substitute difference formulas in iteration formulas. This method cause that our iteration method have not any derivative formulas.

Published in Applied and Computational Mathematics (Volume 3, Issue 4)
DOI 10.11648/j.acm.20140304.14
Page(s) 130-136
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

Newton Method, Hybrid Method, Halley Iteration, Steffenson Method

References
[1] Atkinson, Kendall E. An introduction to numerical analysis, John Wiley & Sons, (1988).
[2] Stoer .J, Bulirsch .R, Introduction to numerical analysis, Springer-Verlag, (1983).
[3] Hildebrand .F.B, Introduction to numerical analysis, Tata McGraw-Hill, (1974).
[4] Nasr-Al-Din, Ide. A new hybrid iteration method for solving algebraic equations, Applied Mathematics and Computation, 195 (2008) 772-774.
[5] 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.
[6] Eskandari .Hamideh, a new numerical solving method for equations of one variable, International Journal of Applied Mathematics and Computer Sciences, 5:3(2009) 183-186.
[7] Cheney .E .W, Kincaid .D, Numerical mathematics and computing, Thomson Learning, 2003.
[8] Stewart .G .W, after notes on numerical analysis, SIAM, 1996.
[9] Pav .Steven E. Numerical Methods Course Notes, 2005.
[10] Quarteroni .A, Sacco .R, Saleri .F, Numerical Mathematics, Springer, 2000.
Cite This Article
  • APA Style

    Hamideh Eskandari. (2014). Generalized Difference Formula for a Nonlinear Equation. Applied and Computational Mathematics, 3(4), 130-136. https://doi.org/10.11648/j.acm.20140304.14

    Copy | Download

    ACS Style

    Hamideh Eskandari. Generalized Difference Formula for a Nonlinear Equation. Appl. Comput. Math. 2014, 3(4), 130-136. doi: 10.11648/j.acm.20140304.14

    Copy | Download

    AMA Style

    Hamideh Eskandari. Generalized Difference Formula for a Nonlinear Equation. Appl Comput Math. 2014;3(4):130-136. doi: 10.11648/j.acm.20140304.14

    Copy | Download

  • @article{10.11648/j.acm.20140304.14,
      author = {Hamideh Eskandari},
      title = {Generalized Difference Formula for a Nonlinear Equation},
      journal = {Applied and Computational Mathematics},
      volume = {3},
      number = {4},
      pages = {130-136},
      doi = {10.11648/j.acm.20140304.14},
      url = {https://doi.org/10.11648/j.acm.20140304.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140304.14},
      abstract = {In this paper, a new iteration scheme is proposed to solve the roots of a nonlinear equation. It is the purpose of this paper to show that, although the new iteration method seems to be of high convergence, the results are promising in that it requires more computation work and even be divergent. In here, we use iteration method that applied derivatives of the first order and the second order; we substitute difference formulas in iteration formulas. This method cause that our iteration method have not any derivative formulas.},
     year = {2014}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Generalized Difference Formula for a Nonlinear Equation
    AU  - Hamideh Eskandari
    Y1  - 2014/07/30
    PY  - 2014
    N1  - https://doi.org/10.11648/j.acm.20140304.14
    DO  - 10.11648/j.acm.20140304.14
    T2  - Applied and Computational Mathematics
    JF  - Applied and Computational Mathematics
    JO  - Applied and Computational Mathematics
    SP  - 130
    EP  - 136
    PB  - Science Publishing Group
    SN  - 2328-5613
    UR  - https://doi.org/10.11648/j.acm.20140304.14
    AB  - In this paper, a new iteration scheme is proposed to solve the roots of a nonlinear equation. It is the purpose of this paper to show that, although the new iteration method seems to be of high convergence, the results are promising in that it requires more computation work and even be divergent. In here, we use iteration method that applied derivatives of the first order and the second order; we substitute difference formulas in iteration formulas. This method cause that our iteration method have not any derivative formulas.
    VL  - 3
    IS  - 4
    ER  - 

    Copy | Download

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

  • Sections