Numerical Methods: Comparative Analysis of Different Methods for Non-Linear Equations
Solving nonlinear equations analytically becomes increasingly complex as functions grow in difficulty or when multiple nonlinear components are involved. This study aims to address that challenge by applying and comparing two well-established numerical methods—the Bisection Method and the False Posi...
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| Format: | Article |
| Language: | English English |
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INTI International University
2025
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| Online Access: | http://eprints.intimal.edu.my/2168/ http://eprints.intimal.edu.my/2168/2/715 http://eprints.intimal.edu.my/2168/3/joit2025_09.pdf |
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| author | Carreon, R.M.M. Culaste, G.C.B. Iradiel, C.A.D. Mozar, R.M. Roy, F.A. Jr Harith, Z. |
| author_facet | Carreon, R.M.M. Culaste, G.C.B. Iradiel, C.A.D. Mozar, R.M. Roy, F.A. Jr Harith, Z. |
| author_sort | Carreon, R.M.M. |
| building | INTI Institutional Repository |
| collection | Online Access |
| description | Solving nonlinear equations analytically becomes increasingly complex as functions grow in difficulty or when multiple nonlinear components are involved. This study aims to address that challenge by applying and comparing two well-established numerical methods—the Bisection Method and the False Position Method—in approximating the real roots of nonlinear equations. These iterative techniques are evaluated based on their accuracy, convergence rate, and computational efficiency. Specifically, the study investigates the number of iterations required, the magnitude of relative errors, and the number of significant digits in the final approximations. The results show that while both methods are capable of reaching the desired tolerance, the False Position Method converges faster and yields a higher accuracy score. The findings contribute to the practical selection of numerical methods by providing a comparative analysis that guides users in choosing the most appropriate technique based on the nature of the nonlinear function. |
| first_indexed | 2025-11-14T11:59:48Z |
| format | Article |
| id | intimal-2168 |
| institution | INTI International University |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-14T11:59:48Z |
| publishDate | 2025 |
| publisher | INTI International University |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | intimal-21682025-08-26T09:21:30Z http://eprints.intimal.edu.my/2168/ Numerical Methods: Comparative Analysis of Different Methods for Non-Linear Equations Carreon, R.M.M. Culaste, G.C.B. Iradiel, C.A.D. Mozar, R.M. Roy, F.A. Jr Harith, Z. Q Science (General) QA Mathematics QA76 Computer software T Technology (General) Solving nonlinear equations analytically becomes increasingly complex as functions grow in difficulty or when multiple nonlinear components are involved. This study aims to address that challenge by applying and comparing two well-established numerical methods—the Bisection Method and the False Position Method—in approximating the real roots of nonlinear equations. These iterative techniques are evaluated based on their accuracy, convergence rate, and computational efficiency. Specifically, the study investigates the number of iterations required, the magnitude of relative errors, and the number of significant digits in the final approximations. The results show that while both methods are capable of reaching the desired tolerance, the False Position Method converges faster and yields a higher accuracy score. The findings contribute to the practical selection of numerical methods by providing a comparative analysis that guides users in choosing the most appropriate technique based on the nature of the nonlinear function. INTI International University 2025-08 Article PeerReviewed text en cc_by_4 http://eprints.intimal.edu.my/2168/2/715 text en cc_by_4 http://eprints.intimal.edu.my/2168/3/joit2025_09.pdf Carreon, R.M.M. and Culaste, G.C.B. and Iradiel, C.A.D. and Mozar, R.M. and Roy, F.A. Jr and Harith, Z. (2025) Numerical Methods: Comparative Analysis of Different Methods for Non-Linear Equations. Journal of Innovation and Technology, 2025 (09). pp. 1-12. ISSN 2805-5179 https://intijournal.intimal.edu.my |
| spellingShingle | Q Science (General) QA Mathematics QA76 Computer software T Technology (General) Carreon, R.M.M. Culaste, G.C.B. Iradiel, C.A.D. Mozar, R.M. Roy, F.A. Jr Harith, Z. Numerical Methods: Comparative Analysis of Different Methods for Non-Linear Equations |
| title | Numerical Methods: Comparative Analysis of Different Methods for Non-Linear Equations |
| title_full | Numerical Methods: Comparative Analysis of Different Methods for Non-Linear Equations |
| title_fullStr | Numerical Methods: Comparative Analysis of Different Methods for Non-Linear Equations |
| title_full_unstemmed | Numerical Methods: Comparative Analysis of Different Methods for Non-Linear Equations |
| title_short | Numerical Methods: Comparative Analysis of Different Methods for Non-Linear Equations |
| title_sort | numerical methods: comparative analysis of different methods for non-linear equations |
| topic | Q Science (General) QA Mathematics QA76 Computer software T Technology (General) |
| url | http://eprints.intimal.edu.my/2168/ http://eprints.intimal.edu.my/2168/ http://eprints.intimal.edu.my/2168/2/715 http://eprints.intimal.edu.my/2168/3/joit2025_09.pdf |