Effective Root-Finding Methods for Nonlinear Equations Based on Multiplicative Calculi
In recent studies, papers related to the multiplicative based numerical methods demonstrate applicability and efficiency of these methods. Numerical root-finding methods are essential for nonlinear equations and have a wide range of applications in science and engineering. Therefore, the idea of roo...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2016/8174610 |
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| author | Ali Özyapıcı Zehra B. Sensoy Tolgay Karanfiller |
| author_facet | Ali Özyapıcı Zehra B. Sensoy Tolgay Karanfiller |
| author_sort | Ali Özyapıcı |
| collection | DOAJ |
| description | In recent studies, papers related to the multiplicative based numerical methods demonstrate applicability and efficiency of these methods. Numerical root-finding methods are essential for nonlinear equations and have a wide range of applications in science and engineering. Therefore, the idea of root-finding methods based on multiplicative and Volterra calculi is self-evident. Newton-Raphson, Halley, Broyden, and perturbed root-finding methods are used in numerical analysis for approximating the roots of nonlinear equations. In this paper, Newton-Raphson methods and consequently perturbed root-finding methods are developed in the frameworks of multiplicative and Volterra calculi. The efficiency of these proposed root-finding methods is exposed by examples, and the results are compared with some ordinary methods. One of the striking results of the proposed method is that the rate of convergence for many problems are considerably larger than the original methods. |
| format | Article |
| id | doaj-art-c8d2d787726943819b6ff6fd211d944e |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-c8d2d787726943819b6ff6fd211d944e2025-02-03T05:53:24ZengWileyJournal of Mathematics2314-46292314-47852016-01-01201610.1155/2016/81746108174610Effective Root-Finding Methods for Nonlinear Equations Based on Multiplicative CalculiAli Özyapıcı0Zehra B. Sensoy1Tolgay Karanfiller2Faculty of Engineering, Cyprus International University, Nicosia, Mersin 10, TurkeyFaculty of Engineering, Cyprus International University, Nicosia, Mersin 10, TurkeyFaculty of Education, Cyprus International University, Nicosia, Mersin 10, TurkeyIn recent studies, papers related to the multiplicative based numerical methods demonstrate applicability and efficiency of these methods. Numerical root-finding methods are essential for nonlinear equations and have a wide range of applications in science and engineering. Therefore, the idea of root-finding methods based on multiplicative and Volterra calculi is self-evident. Newton-Raphson, Halley, Broyden, and perturbed root-finding methods are used in numerical analysis for approximating the roots of nonlinear equations. In this paper, Newton-Raphson methods and consequently perturbed root-finding methods are developed in the frameworks of multiplicative and Volterra calculi. The efficiency of these proposed root-finding methods is exposed by examples, and the results are compared with some ordinary methods. One of the striking results of the proposed method is that the rate of convergence for many problems are considerably larger than the original methods.http://dx.doi.org/10.1155/2016/8174610 |
| spellingShingle | Ali Özyapıcı Zehra B. Sensoy Tolgay Karanfiller Effective Root-Finding Methods for Nonlinear Equations Based on Multiplicative Calculi Journal of Mathematics |
| title | Effective Root-Finding Methods for Nonlinear Equations Based on Multiplicative Calculi |
| title_full | Effective Root-Finding Methods for Nonlinear Equations Based on Multiplicative Calculi |
| title_fullStr | Effective Root-Finding Methods for Nonlinear Equations Based on Multiplicative Calculi |
| title_full_unstemmed | Effective Root-Finding Methods for Nonlinear Equations Based on Multiplicative Calculi |
| title_short | Effective Root-Finding Methods for Nonlinear Equations Based on Multiplicative Calculi |
| title_sort | effective root finding methods for nonlinear equations based on multiplicative calculi |
| url | http://dx.doi.org/10.1155/2016/8174610 |
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