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), 2024. Published by Science Publishing Group |
Nonlinear, Iterative Methods, Convergence, Variable
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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
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
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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Download@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}
}
TY - JOUR T1 - Comparison of Some Iterative Methods of Solving Nonlinear Equations AU - Okorie Charity Ebelechukwu AU - Ben Obakpo Johnson AU - Ali Inalegwu Michael AU - Akuji Terhemba Fidelis Y1 - 2018/07/26 PY - 2018 N1 - https://doi.org/10.11648/j.ijtam.20180402.11 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 SP - 22 EP - 28 PB - Science Publishing Group SN - 2575-5080 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 IS - 2 ER -
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