Generalized Difference Formula for a Nonlinear Equation

Hamideh Eskandari

doi:doi:10.11648/j.acm.20140304.14

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Generalized Difference Formula for a Nonlinear Equation

Hamideh Eskandari

Published in Applied and Computational Mathematics (Volume 3, Issue 4)

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.

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.

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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://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}
}

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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  -

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Author Information

Hamideh Eskandari

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

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Plain Text BibTeX RIS

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

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