Introduction of modified root finding approaches and their comparative study with existing methods
Root-finding in nonlinear equations is a fundamental problem in numerical analysis with applications in mathematics and engineering. Traditional methods like the Bisection and False Position methods have been widely used, but they often face challenges related to convergence speed, stability, and c...
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| Format: | Article |
| Language: | English |
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Institute of Sciences and Technology, University Center Abdelhafid Boussouf, Mila
2025-07-01
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| Series: | Journal of Innovative Applied Mathematics and Computational Sciences |
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| Online Access: | https://jiamcs.centre-univ-mila.dz/index.php/jiamcs/article/view/1921 |
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| _version_ | 1850072080111894528 |
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| author | Haputhanthrige Hashintha Dilan Kumara Samoshi Shanika Haputhanthrige Sachithra Gayashani Withanage Ujitha Imeshan Sanjula Thilakarathne |
| author_facet | Haputhanthrige Hashintha Dilan Kumara Samoshi Shanika Haputhanthrige Sachithra Gayashani Withanage Ujitha Imeshan Sanjula Thilakarathne |
| author_sort | Haputhanthrige Hashintha Dilan Kumara |
| collection | DOAJ |
| description |
Root-finding in nonlinear equations is a fundamental problem in numerical analysis with applications in mathematics and engineering. Traditional methods like the Bisection and False Position methods have been widely used, but they often face challenges related to convergence speed, stability, and computational efficiency. This paper presents two novel numerical root-finding methods that combine the robustness of the Bisection method with the efficiency of the False Position method, improving both convergence rates and stability. Furthermore, we illustrate some numerical applications to discuss error analysis, convergence analysis, and comparisons with existing methods. These findings contribute to the advancement of numerical computation by providing more reliable and efficient root-finding techniques.
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| format | Article |
| id | doaj-art-568ffd301b464a8488d760a5f076261f |
| institution | DOAJ |
| issn | 2773-4196 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Institute of Sciences and Technology, University Center Abdelhafid Boussouf, Mila |
| record_format | Article |
| series | Journal of Innovative Applied Mathematics and Computational Sciences |
| spelling | doaj-art-568ffd301b464a8488d760a5f076261f2025-08-20T02:47:09ZengInstitute of Sciences and Technology, University Center Abdelhafid Boussouf, MilaJournal of Innovative Applied Mathematics and Computational Sciences2773-41962025-07-015110.58205/jiamcs.v5i1.1921Introduction of modified root finding approaches and their comparative study with existing methodsHaputhanthrige Hashintha Dilan Kumara0https://orcid.org/0009-0000-6544-5543Samoshi Shanika1https://orcid.org/0009-0002-9085-9996Haputhanthrige Sachithra Gayashani2https://orcid.org/0009-0005-3575-048XWithanage Ujitha Imeshan3https://orcid.org/0009-0008-1279-9688Sanjula Thilakarathne4https://orcid.org/0009-0000-0378-2851University of Kelaniya, Kelaniya, 11600, Sri LankaSouth Eastern University of Sri Lanka, Oluvil, 32360, Sri LankaUniversity of Sri Jayewardenepura, Nugegoda, 10250, Sri LankaUniversity of Kelaniya, Kelaniya, 11600, Sri LankaUniversity of Kelaniya, Kelaniya, 11600, Sri Lanka Root-finding in nonlinear equations is a fundamental problem in numerical analysis with applications in mathematics and engineering. Traditional methods like the Bisection and False Position methods have been widely used, but they often face challenges related to convergence speed, stability, and computational efficiency. This paper presents two novel numerical root-finding methods that combine the robustness of the Bisection method with the efficiency of the False Position method, improving both convergence rates and stability. Furthermore, we illustrate some numerical applications to discuss error analysis, convergence analysis, and comparisons with existing methods. These findings contribute to the advancement of numerical computation by providing more reliable and efficient root-finding techniques. https://jiamcs.centre-univ-mila.dz/index.php/jiamcs/article/view/1921Root-finding TechniquesBisection methodFalse-Position MethodModified Root-finding MethodsNumerical Algorithms |
| spellingShingle | Haputhanthrige Hashintha Dilan Kumara Samoshi Shanika Haputhanthrige Sachithra Gayashani Withanage Ujitha Imeshan Sanjula Thilakarathne Introduction of modified root finding approaches and their comparative study with existing methods Journal of Innovative Applied Mathematics and Computational Sciences Root-finding Techniques Bisection method False-Position Method Modified Root-finding Methods Numerical Algorithms |
| title | Introduction of modified root finding approaches and their comparative study with existing methods |
| title_full | Introduction of modified root finding approaches and their comparative study with existing methods |
| title_fullStr | Introduction of modified root finding approaches and their comparative study with existing methods |
| title_full_unstemmed | Introduction of modified root finding approaches and their comparative study with existing methods |
| title_short | Introduction of modified root finding approaches and their comparative study with existing methods |
| title_sort | introduction of modified root finding approaches and their comparative study with existing methods |
| topic | Root-finding Techniques Bisection method False-Position Method Modified Root-finding Methods Numerical Algorithms |
| url | https://jiamcs.centre-univ-mila.dz/index.php/jiamcs/article/view/1921 |
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