Comparative study of nonlinear root finding using improvised Secant methods / Nurul Nabilah Rosli … [et al.]
The nonlinear transcendental or algebraic equation problem is one of the important research areas in numerical analysis, and the iterative methods are playing an important role to find approximate solutions. The Secant method is one of the best iterative methods since it only requires a single evalu...
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Universiti Teknologi MARA
2023
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| Online Access: | https://ir.uitm.edu.my/id/eprint/77343/1/77343.pdf https://ir.uitm.edu.my/id/eprint/77343/ https://mjoc.uitm.edu.my/main/ |
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| author | Rosli, Nurul Nabilah Shahari, Nor Azni Mohamad Azraei, Farah Atikah Izaham, Siti Najwa |
| author_facet | Rosli, Nurul Nabilah Shahari, Nor Azni Mohamad Azraei, Farah Atikah Izaham, Siti Najwa |
| author_sort | Rosli, Nurul Nabilah |
| building | Tun Abdul Razak Library |
| collection | Institutional Repository |
| content_provider | Universiti Teknologi Mara |
| content_source | UiTM Institutional Repository |
| continent | Asia |
| country | Malaysia |
| description | The nonlinear transcendental or algebraic equation problem is one of the important research areas in numerical analysis, and the iterative methods are playing an important role to find approximate solutions. The Secant method is one of the best iterative methods since it only requires a single evaluation of function. However, the Secant method has low convergence order, thus many improvised Secant methods have been developed by other researchers. Even though improvise secant method has been developed vastly, comparative study of these methods is relatively scarce, and the novelty of this paper is to assess critical numerical performances of the methods. Therefore, in this study, two algorithms based on the Secant method which are the exponential method, and three-point Secant method were used to compare with the Secant method to evaluate the roots for nonlinear equations. The three methods were tested using different initial values in various transcendental functions such as polynomial, exponential, logarithm, trigonometric and some combinations of linear, exponential, polynomial, and trigonometric functions to determine the best method among three methods and to determine the behavior of these method. All the computation results were developed using Graphical User Interface (GUI) in MATLAB environment to get the results and as the visual indicator representations. The obtained results show that the three-point Secant method has the least number of iterations than the Secant method and exponential method in six numerical results. Conclusively, the three-point Secant method is the best iterative method since the method converged to the roots faster than other two. |
| format | Article |
| id | my.uitm.ir-77343 |
| institution | Universiti Teknologi Mara |
| language | en |
| publishDate | 2023 |
| publisher | Universiti Teknologi MARA |
| record_format | eprints |
| spelling | my.uitm.ir-773432023-05-09T08:49:55Z https://ir.uitm.edu.my/id/eprint/77343/ Comparative study of nonlinear root finding using improvised Secant methods / Nurul Nabilah Rosli … [et al.] mjoc Rosli, Nurul Nabilah Shahari, Nor Azni Mohamad Azraei, Farah Atikah Izaham, Siti Najwa Algebra The nonlinear transcendental or algebraic equation problem is one of the important research areas in numerical analysis, and the iterative methods are playing an important role to find approximate solutions. The Secant method is one of the best iterative methods since it only requires a single evaluation of function. However, the Secant method has low convergence order, thus many improvised Secant methods have been developed by other researchers. Even though improvise secant method has been developed vastly, comparative study of these methods is relatively scarce, and the novelty of this paper is to assess critical numerical performances of the methods. Therefore, in this study, two algorithms based on the Secant method which are the exponential method, and three-point Secant method were used to compare with the Secant method to evaluate the roots for nonlinear equations. The three methods were tested using different initial values in various transcendental functions such as polynomial, exponential, logarithm, trigonometric and some combinations of linear, exponential, polynomial, and trigonometric functions to determine the best method among three methods and to determine the behavior of these method. All the computation results were developed using Graphical User Interface (GUI) in MATLAB environment to get the results and as the visual indicator representations. The obtained results show that the three-point Secant method has the least number of iterations than the Secant method and exponential method in six numerical results. Conclusively, the three-point Secant method is the best iterative method since the method converged to the roots faster than other two. Universiti Teknologi MARA 2023-04 Article PeerReviewed text en https://ir.uitm.edu.my/id/eprint/77343/1/77343.pdf Comparative study of nonlinear root finding using improvised Secant methods / Nurul Nabilah Rosli … [et al.]. (2023) Malaysian Journal of Computing (MJoC) <https://ir.uitm.edu.my/view/publication/Malaysian_Journal_of_Computing_=28MJoC=29/>, 8 (1): 7. pp. 1332-1348. ISSN 2600-8238 https://mjoc.uitm.edu.my/main/ |
| spellingShingle | Algebra Rosli, Nurul Nabilah Shahari, Nor Azni Mohamad Azraei, Farah Atikah Izaham, Siti Najwa Comparative study of nonlinear root finding using improvised Secant methods / Nurul Nabilah Rosli … [et al.] |
| title | Comparative study of nonlinear root finding using improvised Secant methods / Nurul Nabilah Rosli … [et al.] |
| title_full | Comparative study of nonlinear root finding using improvised Secant methods / Nurul Nabilah Rosli … [et al.] |
| title_fullStr | Comparative study of nonlinear root finding using improvised Secant methods / Nurul Nabilah Rosli … [et al.] |
| title_full_unstemmed | Comparative study of nonlinear root finding using improvised Secant methods / Nurul Nabilah Rosli … [et al.] |
| title_short | Comparative study of nonlinear root finding using improvised Secant methods / Nurul Nabilah Rosli … [et al.] |
| title_sort | comparative study of nonlinear root finding using improvised secant methods / nurul nabilah rosli … [et al.] |
| topic | Algebra |
| url | https://ir.uitm.edu.my/id/eprint/77343/1/77343.pdf https://ir.uitm.edu.my/id/eprint/77343/ https://mjoc.uitm.edu.my/main/ |
| url_provider | http://ir.uitm.edu.my/ |