Comparative Study of Numerical Methods for Solving Non-linear Equations Using Manual Computation

Isaac Azure; Golbert Aloliga; Louis Doabil

doi:doi:10.11648/j.ml.20190504.11

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Comparative Study of Numerical Methods for Solving Non-linear Equations Using Manual Computation

Isaac Azure, Golbert Aloliga, Louis Doabil

Received: 30 June 2019 Accepted: 25 December 2019 Published: 8 January 2020

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Abstract

This paper aims at comparing the performance in relation to the rate of convergence of five numerical methods namely, the Bisection method, Newton Raphson method, Regula Falsi method, Secant method, and Fixed Point Iteration method. A manual computational algorithm is developed for each of the methods and each one of them is employed to solve a root - finding problem manually with the help of an TI - inspire instrument. The outcome of the computations showed that all methods converged to an exact root of 1.56155, however the Bisection method converged at the 14th iteration, Fixed Point Iterative Method converged at 7th iteration, Secant method converged at the 5th iteration and Regula Falsi and Newton Raphson methods converged at the 2nd iteration, suggesting that Newton Raphson and Regula Falsi methods are more efficient in computing the roots of a nonlinear quadratic equation.

DOI	10.11648/j.ml.20190504.11
Published in	Mathematics Letters (Volume 5, Issue 4, December 2019)
Page(s)	41-46
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

Numerical Methods, Convergence, Root, Iteration, Manual Computation, Nonlinear Equations

References

[1]	Abdul-Hassan, N. Y. (2016). New Predictor-Corrector Iterative Methods with Twelfth-Order Convergence for Solving Nonlinear Equations. American Journal of Applied Mathematics, 4 (4), 175-180.
[2]	Adegoke, T. M., Adegoke, G. K., Yahya, A. M., & Oduwole, H. K. (2018). Comparative Study of Some Numerical Iterations Using Zero Truncated Poisson Distribution. 1–30.
[3]	Ahmad, A. G. (2015). Comparative Study of Bisection and Newton-Rhapson Methods of Root-Finding Problems. International Journal of Mathematics Trends and Technology, 19 (2).
[4]	Biswa, N. D. (2012). Lecture Notes on Numerical Solution of Root − Finding Problems MATH 435.
[5]	Ebelechukwu, O. C., Johnson, B. O., Michael, A. I., & Fidelis, A. T. (2018). Comparison of Some Iterative Methods of Solving Nonlinear Equations. International Journal of Theoretical and Applied Mathematics, 4 (2), 22.
[6]	Ehiwario, J. C., & Aghamie, S. O. (2014). Comparative Study of Bisection, Newton-Raphson and Secant Methods of Root-Finding Problems. IOSR Journal of Engineering (IOSRJEN), 4 (04).
[7]	Gomes, A., & Morgado, J. (2013). A generalized regula falsi method for finding zeros and extrema of real functions. Mathematical Problems in Engineering, 2013.
[8]	Kumar, R. (2015). Comparative Analysis of Convergence of Various Numerical Methods. 6 (June), 290–297.
[9]	Moheuddin, M. M., Uddin, M. J., & Kowsher, M. A New STUDY TO FIND OUT THE BEST COMPUTATIONAL METHOD FOR SOLVING THE NONLINEAR EQUATION.
[10]	Steven, C. C and Raymond, P. C (2015). Numerical Methods for Engineers.
[11]	Srivastava, R. B., & Srivastava, S. (2011). Comparison of Numerical Rate of Convergence of Bisection, Newton-Raphson's and Secant Methods. Journal of Chemical, Biological and Physical Sciences (JCBPS), 2 (1), 472.

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APA Style

Isaac Azure, Golbert Aloliga, Louis Doabil. (2020). Comparative Study of Numerical Methods for Solving Non-linear Equations Using Manual Computation. Mathematics Letters, 5(4), 41-46. https://doi.org/10.11648/j.ml.20190504.11

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ACS Style

Isaac Azure; Golbert Aloliga; Louis Doabil. Comparative Study of Numerical Methods for Solving Non-linear Equations Using Manual Computation. Math. Lett. 2020, 5(4), 41-46. doi: 10.11648/j.ml.20190504.11

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AMA Style

Isaac Azure, Golbert Aloliga, Louis Doabil. Comparative Study of Numerical Methods for Solving Non-linear Equations Using Manual Computation. Math Lett. 2020;5(4):41-46. doi: 10.11648/j.ml.20190504.11

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@article{10.11648/j.ml.20190504.11,
  author = {Isaac Azure and Golbert Aloliga and Louis Doabil},
  title = {Comparative Study of Numerical Methods for Solving Non-linear Equations Using Manual Computation},
  journal = {Mathematics Letters},
  volume = {5},
  number = {4},
  pages = {41-46},
  doi = {10.11648/j.ml.20190504.11},
  url = {https://doi.org/10.11648/j.ml.20190504.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20190504.11},
  abstract = {This paper aims at comparing the performance in relation to the rate of convergence of five numerical methods namely, the Bisection method, Newton Raphson method, Regula Falsi method, Secant method, and Fixed Point Iteration method. A manual computational algorithm is developed for each of the methods and each one of them is employed to solve a root - finding problem manually with the help of an TI - inspire instrument. The outcome of the computations showed that all methods converged to an exact root of 1.56155, however the Bisection method converged at the 14th iteration, Fixed Point Iterative Method converged at 7th iteration, Secant method converged at the 5th iteration and Regula Falsi and Newton Raphson methods converged at the 2nd iteration, suggesting that Newton Raphson and Regula Falsi methods are more efficient in computing the roots of a nonlinear quadratic equation.},
 year = {2020}
}

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TY  - JOUR
T1  - Comparative Study of Numerical Methods for Solving Non-linear Equations Using Manual Computation
AU  - Isaac Azure
AU  - Golbert Aloliga
AU  - Louis Doabil
Y1  - 2020/01/08
PY  - 2020
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DO  - 10.11648/j.ml.20190504.11
T2  - Mathematics Letters
JF  - Mathematics Letters
JO  - Mathematics Letters
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EP  - 46
PB  - Science Publishing Group
SN  - 2575-5056
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AB  - This paper aims at comparing the performance in relation to the rate of convergence of five numerical methods namely, the Bisection method, Newton Raphson method, Regula Falsi method, Secant method, and Fixed Point Iteration method. A manual computational algorithm is developed for each of the methods and each one of them is employed to solve a root - finding problem manually with the help of an TI - inspire instrument. The outcome of the computations showed that all methods converged to an exact root of 1.56155, however the Bisection method converged at the 14th iteration, Fixed Point Iterative Method converged at 7th iteration, Secant method converged at the 5th iteration and Regula Falsi and Newton Raphson methods converged at the 2nd iteration, suggesting that Newton Raphson and Regula Falsi methods are more efficient in computing the roots of a nonlinear quadratic equation.
VL  - 5
IS  - 4
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Author Information

Isaac Azure

Department of Computer Science, Regentropfen College of Applied Sciences, Bolgatanga, Ghana
Golbert Aloliga

Mathematics Department, St. Vincent College of Education, Yendi, Ghana
Louis Doabil

Business School, Ghana Institute of Management & Public Administration, Accra, Ghana

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APA Style

Isaac Azure, Golbert Aloliga, Louis Doabil. (2020). Comparative Study of Numerical Methods for Solving Non-linear Equations Using Manual Computation. Mathematics Letters, 5(4), 41-46. https://doi.org/10.11648/j.ml.20190504.11

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ACS Style

Isaac Azure; Golbert Aloliga; Louis Doabil. Comparative Study of Numerical Methods for Solving Non-linear Equations Using Manual Computation. Math. Lett. 2020, 5(4), 41-46. doi: 10.11648/j.ml.20190504.11

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AMA Style

Isaac Azure, Golbert Aloliga, Louis Doabil. Comparative Study of Numerical Methods for Solving Non-linear Equations Using Manual Computation. Math Lett. 2020;5(4):41-46. doi: 10.11648/j.ml.20190504.11

Copy | Download

@article{10.11648/j.ml.20190504.11,
  author = {Isaac Azure and Golbert Aloliga and Louis Doabil},
  title = {Comparative Study of Numerical Methods for Solving Non-linear Equations Using Manual Computation},
  journal = {Mathematics Letters},
  volume = {5},
  number = {4},
  pages = {41-46},
  doi = {10.11648/j.ml.20190504.11},
  url = {https://doi.org/10.11648/j.ml.20190504.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20190504.11},
  abstract = {This paper aims at comparing the performance in relation to the rate of convergence of five numerical methods namely, the Bisection method, Newton Raphson method, Regula Falsi method, Secant method, and Fixed Point Iteration method. A manual computational algorithm is developed for each of the methods and each one of them is employed to solve a root - finding problem manually with the help of an TI - inspire instrument. The outcome of the computations showed that all methods converged to an exact root of 1.56155, however the Bisection method converged at the 14th iteration, Fixed Point Iterative Method converged at 7th iteration, Secant method converged at the 5th iteration and Regula Falsi and Newton Raphson methods converged at the 2nd iteration, suggesting that Newton Raphson and Regula Falsi methods are more efficient in computing the roots of a nonlinear quadratic equation.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Comparative Study of Numerical Methods for Solving Non-linear Equations Using Manual Computation
AU  - Isaac Azure
AU  - Golbert Aloliga
AU  - Louis Doabil
Y1  - 2020/01/08
PY  - 2020
N1  - https://doi.org/10.11648/j.ml.20190504.11
DO  - 10.11648/j.ml.20190504.11
T2  - Mathematics Letters
JF  - Mathematics Letters
JO  - Mathematics Letters
SP  - 41
EP  - 46
PB  - Science Publishing Group
SN  - 2575-5056
UR  - https://doi.org/10.11648/j.ml.20190504.11
AB  - This paper aims at comparing the performance in relation to the rate of convergence of five numerical methods namely, the Bisection method, Newton Raphson method, Regula Falsi method, Secant method, and Fixed Point Iteration method. A manual computational algorithm is developed for each of the methods and each one of them is employed to solve a root - finding problem manually with the help of an TI - inspire instrument. The outcome of the computations showed that all methods converged to an exact root of 1.56155, however the Bisection method converged at the 14th iteration, Fixed Point Iterative Method converged at 7th iteration, Secant method converged at the 5th iteration and Regula Falsi and Newton Raphson methods converged at the 2nd iteration, suggesting that Newton Raphson and Regula Falsi methods are more efficient in computing the roots of a nonlinear quadratic equation.
VL  - 5
IS  - 4
ER  -

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