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Comparison of Some Iterative Methods of Solving Nonlinear Equations

Received: 23 December 2017     Accepted: 15 May 2018     Published: 26 July 2018
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Abstract

This work focuses on nonlinear equation (x) = 0, it is noted that no or little attention is given to nonlinear equations. The purpose of this work is to determine the best method of solving nonlinear equations. The work outlined four methods of solving nonlinear equations. Unlike linear equations, most nonlinear equations cannot be solved in finite number of steps. Iterative methods are being used to solve nonlinear equations. The cost of solving nonlinear equations problems depend on both the cost per iteration and the number of iterations required. Derivations of each of the methods were obtained. An example was illustrated to show the results of all the four methods and the results were collected, tabulated and analyzed in terms of their errors and convergence respectively. The results were also presented in form of graphs. The implication is that the higher the rate of convergence determines how fast it will get to the approximate root or solution of the equation. Thus, it was recommended that the Newton’s method is the best method of solving the nonlinear equation f(x) = 0 containing one variable because of its high rate of convergence.

Published in International Journal of Theoretical and Applied Mathematics (Volume 4, Issue 2)
DOI 10.11648/j.ijtam.20180402.11
Page(s) 22-28
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), 2018. Published by Science Publishing Group

Keywords

Nonlinear, Iterative Methods, Convergence, Variable

References
[1] Aisha H.A; Fatima W.L; Waziri M.Y. (2014). International journal of computer application, vol 98business dictionary. (2016). www.Business dictionary.com. copyright 2001-2016, web finance, In
[2] Dass H.K. and Rajnish Verma (2012).Higher Engineering Mathematics. Published by S. Chand and Company ltd (AN ISO 90012008 Company). Ram New Delhi- 110055.
[3] Deborah Dent and Marcin Paaprzycki. (2000).Recent advances in solvers for nonlinear algebraic Equations. School of mathematical sciences, University of Southern Mississippi Hattiesburg.
[4] Erwin Kreysig (2011). Advance Engineering Mathematics. Tenth edition. Published by John Wileyand sons, inc.
[5] Free dictionary. (2011). American Heritage dictionary of the English language, fifth edition, copyright by Houghton Mifflin Harcourt publishing company.
[6] Giberto E. Urroz. (2004).Solution of nonlinear equations. A paper document on solving nonlinearequation using Matlab.
[7] John Rice (1969), Approximation of functions: Nonlinear and Multivariate Theory, Publisher; Addison–Wesley Publishing Company.
[8] Kandasamy P. (2012). Numerical methods. Published by S. Chand and company ltd (AN ISO 9001; 2000 Company). Ram Nagar, new-Delhi – 110 055
[9] Masoud Allame. (2001). A new method for solving nonlinear equations by Taylor’s Expansion. Conference paper, Islamic Azad University. Numerical analysis Encyclopedia Britannica online. .
[10] Sara T.M. Suleiman. (2009).Solving Nonlinear equations using methods in the Halley class. Thesis for the degree of master of sciences.
[11] Sona Taheri, Musa Mammadov (2012), Solving Systems of Nonlinear Equations using a Globally Convergent Optimization Algorithm Transaction on Evolutionary Algorithm and Nonlinear Optimization ISSN: 2229-8711 Online Publication, June 2012www.pcoglobal.com/gjto.htm
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  • APA Style

    Okorie Charity Ebelechukwu, Ben Obakpo Johnson, Ali Inalegwu Michael, Akuji Terhemba Fidelis. (2018). Comparison of Some Iterative Methods of Solving Nonlinear Equations. International Journal of Theoretical and Applied Mathematics, 4(2), 22-28. https://doi.org/10.11648/j.ijtam.20180402.11

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    ACS Style

    Okorie Charity Ebelechukwu; Ben Obakpo Johnson; Ali Inalegwu Michael; Akuji Terhemba Fidelis. Comparison of Some Iterative Methods of Solving Nonlinear Equations. Int. J. Theor. Appl. Math. 2018, 4(2), 22-28. doi: 10.11648/j.ijtam.20180402.11

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    AMA Style

    Okorie Charity Ebelechukwu, Ben Obakpo Johnson, Ali Inalegwu Michael, Akuji Terhemba Fidelis. Comparison of Some Iterative Methods of Solving Nonlinear Equations. Int J Theor Appl Math. 2018;4(2):22-28. doi: 10.11648/j.ijtam.20180402.11

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  • @article{10.11648/j.ijtam.20180402.11,
      author = {Okorie Charity Ebelechukwu and Ben Obakpo Johnson and Ali Inalegwu Michael and Akuji Terhemba Fidelis},
      title = {Comparison of Some Iterative Methods of Solving Nonlinear Equations},
      journal = {International Journal of Theoretical and Applied Mathematics},
      volume = {4},
      number = {2},
      pages = {22-28},
      doi = {10.11648/j.ijtam.20180402.11},
      url = {https://doi.org/10.11648/j.ijtam.20180402.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20180402.11},
      abstract = {This work focuses on nonlinear equation (x) = 0, it is noted that no or little attention is given to nonlinear equations. The purpose of this work is to determine the best method of solving nonlinear equations. The work outlined four methods of solving nonlinear equations. Unlike linear equations, most nonlinear equations cannot be solved in finite number of steps. Iterative methods are being used to solve nonlinear equations. The cost of solving nonlinear equations problems depend on both the cost per iteration and the number of iterations required. Derivations of each of the methods were obtained. An example was illustrated to show the results of all the four methods and the results were collected, tabulated and analyzed in terms of their errors and convergence respectively. The results were also presented in form of graphs. The implication is that the higher the rate of convergence determines how fast it will get to the approximate root or solution of the equation. Thus, it was recommended that the Newton’s method is the best method of solving the nonlinear equation f(x) = 0 containing one variable because of its high rate of convergence.},
     year = {2018}
    }
    

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    AU  - Okorie Charity Ebelechukwu
    AU  - Ben Obakpo Johnson
    AU  - Ali Inalegwu Michael
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    Y1  - 2018/07/26
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    DO  - 10.11648/j.ijtam.20180402.11
    T2  - International Journal of Theoretical and Applied Mathematics
    JF  - International Journal of Theoretical and Applied Mathematics
    JO  - International Journal of Theoretical and Applied Mathematics
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    PB  - Science Publishing Group
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    UR  - https://doi.org/10.11648/j.ijtam.20180402.11
    AB  - This work focuses on nonlinear equation (x) = 0, it is noted that no or little attention is given to nonlinear equations. The purpose of this work is to determine the best method of solving nonlinear equations. The work outlined four methods of solving nonlinear equations. Unlike linear equations, most nonlinear equations cannot be solved in finite number of steps. Iterative methods are being used to solve nonlinear equations. The cost of solving nonlinear equations problems depend on both the cost per iteration and the number of iterations required. Derivations of each of the methods were obtained. An example was illustrated to show the results of all the four methods and the results were collected, tabulated and analyzed in terms of their errors and convergence respectively. The results were also presented in form of graphs. The implication is that the higher the rate of convergence determines how fast it will get to the approximate root or solution of the equation. Thus, it was recommended that the Newton’s method is the best method of solving the nonlinear equation f(x) = 0 containing one variable because of its high rate of convergence.
    VL  - 4
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Author Information
  • Department of Mathematics and Statistics, Faculty of Pure and Applied Sciences, Federal University, Wukari, Nigeria

  • Department of Mathematics and Statistics, Faculty of Pure and Applied Sciences, Federal University, Wukari, Nigeria

  • Department of Mathematics and Statistics, Faculty of Pure and Applied Sciences, Federal University, Wukari, Nigeria

  • Department of Mathematics and Statistics, Faculty of Pure and Applied Sciences, Federal University, Wukari, Nigeria

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