An Analysis of Solutions of Nonlinear Equations Using AI Inspired Mathematical Packages

Isaac Azure

doi:doi:10.11648/j.ijssam.20230802.12

| Peer-Reviewed

An Analysis of Solutions of Nonlinear Equations Using AI Inspired Mathematical Packages

Isaac Azure

Published in International Journal of Systems Science and Applied Mathematics (Volume 8, Issue 2)

Received: 11 August 2023 Accepted: 29 August 2023 Published: 8 September 2023

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

In the era of Artificial Intelligence (AI), achieving precise solutions for nonlinear equations has been considerably streamlined, thanks to the advancement of various mathematical tools designed for numerical computations. However, as the utilization of these mathematical software continues to rise, researchers are keen to ascertain the optimal choice among these tools based on their outcome when applied to solving nonlinear equations. This study addresses this question by undertaking a comparative analysis of three prominent mathematical software packages Python, Scilab, and MATLAB using two numerical approaches: Newton-Raphson and Secant. By employing the Newton-Raphson and Secant methods to solve five benchmark problems, this paper assesses the performance of the aforementioned mathematical tools. Notably, the outcomes underscore the competence of all three software options in yielding suitable approximations of the problem's root solutions. In particular, Python stands out for its ability to achieve this while utilizing the fewest iterations and minimizing computational time. As a result, among the three tools investigated, Python emerges as the most favorable choice, considering its efficiency and accuracy. Furthermore, this research validates the robustness of the Newton-Raphson approach over the Secant method, given its capability to efficiently converge to the solutions with the minimal iteration count across the benchmark problems. This finding highlights the superiority of the Newton-Raphson method as a more efficient and reliable technique for solving the considered benchmark problems.

Published in	International Journal of Systems Science and Applied Mathematics (Volume 8, Issue 2)
DOI	10.11648/j.ijssam.20230802.12
Page(s)	23-30
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

Nonlinear Equations, Artificial Intelligence (AI), MATLAB, SCILAB, Python, Secant Method, Newton Raphson Method

References

[1]	Ahmad, A. G. (2015). Comparative Study of Bisection and Newton-Raphson Methods of Root-Finding Problems. International Journal of Mathematics Trends and Technology, 19 (2).
[2]	Azure, I., Aloliga, G., & Doabil, L. (2019). Comparative Study of Numerical Methods for Solving Non-linear Equations Using Manual Computation. Mathematics Letters, 5 (4), 41-46. doi: 10.11648/j.ml.20190504.11.
[3]	Biswa, N. D. (2012). Lecture Notes on Numerical Solution of Root-Finding Problems MATH 435.
[4]	Downey, A. B. (2015). Think Python: How to Think Like a Computer Scientist. Green Tea Press. Available online: http://greenteapress.com/thinkpython2/html/index.html
[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]	Hanselman, D. C., & Littlefield, B. L. (2018). The Art of MATLAB. Cambridge University Press.
[8]	Hahn, B., & Valentine, D. T. (2020). Essential MATLAB for Engineers and Scientists. Academic Press.
[9]	Kazemi, M., Deep, A., & Nieto, J. (2023). An existence result with numerical solution of nonlinear fractional integral equations. Mathematical Methods in the Applied Sciences.
[10]	King, A. P., & Aljabar, P. (2017). MATLAB Programming for Biomedical Engineers and Scientists. Academic Press.
[11]	Mahdy, A. M. S. (2022). A numerical method for solving the nonlinear equations of Emden-Fowler models. Journal of Ocean Engineering and Science.
[12]	Mikac, M., Logožar, R., & Horvatić, M. (2022). Performance Comparison of Open Source and Commercial Computing Tools in Educational and Other Use—Scilab vs. MATLAB. Tehnički glasnik, 16 (4), 509-518.
[13]	Nagar, S. (2021). Introduction to Scilab. Notion Press.
[14]	Python Software Foundation. (2021). Python 3.10.0 Documentation. Retrieved from https://docs.python.org/3/
[15]	RASHEED, M., Rashid, A., Rashid, T., Hamed, S. H. A., & AL-Farttoosi, O. A. A. (2021). Application of Numerical Analysis for Solving Nonlinear Equation. Journal of Al-Qadisiyah for computer science and mathematics, 13 (3), Page-70.
[16]	RASHEED, M., SHIHAB, S., Rashid, A., Rashid, T., Hamed, S. H. A., & Aldulaimi, M. A. H. (2021). An Iterative Method to Solve Nonlinear Equation. Journal of Al-Qadisiyah for Computer Science and Mathematics, 13 (2), Page-87.
[17]	Sheth, T. (2018). Scilab: A Practical Introduction to Programming and Problem Solving. CRC Press.
[18]	Sizemore, J., & Mueller, J. P. (2019). MATLAB For Dummies. Wiley.
[19]	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.
[20]	Vishwanatha, J. S., Swamy, R. S., Mahesh, G., & Gouda, H. V. (2023). A toolkit for computational fluid dynamics using spectral element method in Scilab. Materials Today: Proceedings.

Cite This Article

Plain Text BibTeX RIS

APA Style

Isaac Azure. (2023). An Analysis of Solutions of Nonlinear Equations Using AI Inspired Mathematical Packages. International Journal of Systems Science and Applied Mathematics, 8(2), 23-30. https://doi.org/10.11648/j.ijssam.20230802.12

Copy | Download

ACS Style

Isaac Azure. An Analysis of Solutions of Nonlinear Equations Using AI Inspired Mathematical Packages. Int. J. Syst. Sci. Appl. Math. 2023, 8(2), 23-30. doi: 10.11648/j.ijssam.20230802.12

Copy | Download

AMA Style

Isaac Azure. An Analysis of Solutions of Nonlinear Equations Using AI Inspired Mathematical Packages. Int J Syst Sci Appl Math. 2023;8(2):23-30. doi: 10.11648/j.ijssam.20230802.12

Copy | Download

@article{10.11648/j.ijssam.20230802.12,
  author = {Isaac Azure},
  title = {An Analysis of Solutions of Nonlinear Equations Using AI Inspired Mathematical Packages},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {8},
  number = {2},
  pages = {23-30},
  doi = {10.11648/j.ijssam.20230802.12},
  url = {https://doi.org/10.11648/j.ijssam.20230802.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20230802.12},
  abstract = {In the era of Artificial Intelligence (AI), achieving precise solutions for nonlinear equations has been considerably streamlined, thanks to the advancement of various mathematical tools designed for numerical computations. However, as the utilization of these mathematical software continues to rise, researchers are keen to ascertain the optimal choice among these tools based on their outcome when applied to solving nonlinear equations. This study addresses this question by undertaking a comparative analysis of three prominent mathematical software packages Python, Scilab, and MATLAB using two numerical approaches: Newton-Raphson and Secant. By employing the Newton-Raphson and Secant methods to solve five benchmark problems, this paper assesses the performance of the aforementioned mathematical tools. Notably, the outcomes underscore the competence of all three software options in yielding suitable approximations of the problem's root solutions. In particular, Python stands out for its ability to achieve this while utilizing the fewest iterations and minimizing computational time. As a result, among the three tools investigated, Python emerges as the most favorable choice, considering its efficiency and accuracy. Furthermore, this research validates the robustness of the Newton-Raphson approach over the Secant method, given its capability to efficiently converge to the solutions with the minimal iteration count across the benchmark problems. This finding highlights the superiority of the Newton-Raphson method as a more efficient and reliable technique for solving the considered benchmark problems.},
 year = {2023}
}

Copy | Download

TY  - JOUR
T1  - An Analysis of Solutions of Nonlinear Equations Using AI Inspired Mathematical Packages
AU  - Isaac Azure
Y1  - 2023/09/08
PY  - 2023
N1  - https://doi.org/10.11648/j.ijssam.20230802.12
DO  - 10.11648/j.ijssam.20230802.12
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 23
EP  - 30
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20230802.12
AB  - In the era of Artificial Intelligence (AI), achieving precise solutions for nonlinear equations has been considerably streamlined, thanks to the advancement of various mathematical tools designed for numerical computations. However, as the utilization of these mathematical software continues to rise, researchers are keen to ascertain the optimal choice among these tools based on their outcome when applied to solving nonlinear equations. This study addresses this question by undertaking a comparative analysis of three prominent mathematical software packages Python, Scilab, and MATLAB using two numerical approaches: Newton-Raphson and Secant. By employing the Newton-Raphson and Secant methods to solve five benchmark problems, this paper assesses the performance of the aforementioned mathematical tools. Notably, the outcomes underscore the competence of all three software options in yielding suitable approximations of the problem's root solutions. In particular, Python stands out for its ability to achieve this while utilizing the fewest iterations and minimizing computational time. As a result, among the three tools investigated, Python emerges as the most favorable choice, considering its efficiency and accuracy. Furthermore, this research validates the robustness of the Newton-Raphson approach over the Secant method, given its capability to efficiently converge to the solutions with the minimal iteration count across the benchmark problems. This finding highlights the superiority of the Newton-Raphson method as a more efficient and reliable technique for solving the considered benchmark problems.
VL  - 8
IS  - 2
ER  -

Copy | Download

Author Information

Isaac Azure

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

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Isaac Azure. (2023). An Analysis of Solutions of Nonlinear Equations Using AI Inspired Mathematical Packages. International Journal of Systems Science and Applied Mathematics, 8(2), 23-30. https://doi.org/10.11648/j.ijssam.20230802.12

Copy | Download

ACS Style

Isaac Azure. An Analysis of Solutions of Nonlinear Equations Using AI Inspired Mathematical Packages. Int. J. Syst. Sci. Appl. Math. 2023, 8(2), 23-30. doi: 10.11648/j.ijssam.20230802.12

Copy | Download

AMA Style

Isaac Azure. An Analysis of Solutions of Nonlinear Equations Using AI Inspired Mathematical Packages. Int J Syst Sci Appl Math. 2023;8(2):23-30. doi: 10.11648/j.ijssam.20230802.12

Copy | Download

@article{10.11648/j.ijssam.20230802.12,
  author = {Isaac Azure},
  title = {An Analysis of Solutions of Nonlinear Equations Using AI Inspired Mathematical Packages},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {8},
  number = {2},
  pages = {23-30},
  doi = {10.11648/j.ijssam.20230802.12},
  url = {https://doi.org/10.11648/j.ijssam.20230802.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20230802.12},
  abstract = {In the era of Artificial Intelligence (AI), achieving precise solutions for nonlinear equations has been considerably streamlined, thanks to the advancement of various mathematical tools designed for numerical computations. However, as the utilization of these mathematical software continues to rise, researchers are keen to ascertain the optimal choice among these tools based on their outcome when applied to solving nonlinear equations. This study addresses this question by undertaking a comparative analysis of three prominent mathematical software packages Python, Scilab, and MATLAB using two numerical approaches: Newton-Raphson and Secant. By employing the Newton-Raphson and Secant methods to solve five benchmark problems, this paper assesses the performance of the aforementioned mathematical tools. Notably, the outcomes underscore the competence of all three software options in yielding suitable approximations of the problem's root solutions. In particular, Python stands out for its ability to achieve this while utilizing the fewest iterations and minimizing computational time. As a result, among the three tools investigated, Python emerges as the most favorable choice, considering its efficiency and accuracy. Furthermore, this research validates the robustness of the Newton-Raphson approach over the Secant method, given its capability to efficiently converge to the solutions with the minimal iteration count across the benchmark problems. This finding highlights the superiority of the Newton-Raphson method as a more efficient and reliable technique for solving the considered benchmark problems.},
 year = {2023}
}

Copy | Download

TY  - JOUR
T1  - An Analysis of Solutions of Nonlinear Equations Using AI Inspired Mathematical Packages
AU  - Isaac Azure
Y1  - 2023/09/08
PY  - 2023
N1  - https://doi.org/10.11648/j.ijssam.20230802.12
DO  - 10.11648/j.ijssam.20230802.12
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 23
EP  - 30
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20230802.12
AB  - In the era of Artificial Intelligence (AI), achieving precise solutions for nonlinear equations has been considerably streamlined, thanks to the advancement of various mathematical tools designed for numerical computations. However, as the utilization of these mathematical software continues to rise, researchers are keen to ascertain the optimal choice among these tools based on their outcome when applied to solving nonlinear equations. This study addresses this question by undertaking a comparative analysis of three prominent mathematical software packages Python, Scilab, and MATLAB using two numerical approaches: Newton-Raphson and Secant. By employing the Newton-Raphson and Secant methods to solve five benchmark problems, this paper assesses the performance of the aforementioned mathematical tools. Notably, the outcomes underscore the competence of all three software options in yielding suitable approximations of the problem's root solutions. In particular, Python stands out for its ability to achieve this while utilizing the fewest iterations and minimizing computational time. As a result, among the three tools investigated, Python emerges as the most favorable choice, considering its efficiency and accuracy. Furthermore, this research validates the robustness of the Newton-Raphson approach over the Secant method, given its capability to efficiently converge to the solutions with the minimal iteration count across the benchmark problems. This finding highlights the superiority of the Newton-Raphson method as a more efficient and reliable technique for solving the considered benchmark problems.
VL  - 8
IS  - 2
ER  -

Copy | Download