International Journal of Systems Science and Applied Mathematics

Submit a Manuscript

Publishing with us to make your research visible to the widest possible audience.

Propose a Special Issue

Building a community of authors and readers to discuss the latest research and develop new ideas.

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

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.

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

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

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

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

Copyright © 2023 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.