Applied and Computational Mathematics

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Generalized Difference Formula for a Nonlinear Equation

Received: 12 July 2014    Accepted: 22 July 2014    Published: 30 July 2014
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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.

DOI 10.11648/j.acm.20140304.14
Published in Applied and Computational Mathematics (Volume 3, Issue 4, August 2014)
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), 2024. 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.
Author Information
  • Department of Mathematics, Payame Noor University, I. R. Iran

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  • 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

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    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

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    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

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  • @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://download.sciencepg.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}
    }
    

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