Optimal Algorithms for Nonlinear Equations with Applications and Their Dynamics
In the present work, we introduce two novel root-finding algorithms for nonlinear scalar equations. Among these algorithms, the second one is optimal according to Kung-Traub’s conjecture. It is established that the newly proposed algorithms bear the fourth- and sixth-order of convergence. To show th...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2022/9705690 |
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| author | Amir Naseem M. A. Rehman Nasr Al Din Ide |
| author_facet | Amir Naseem M. A. Rehman Nasr Al Din Ide |
| author_sort | Amir Naseem |
| collection | DOAJ |
| description | In the present work, we introduce two novel root-finding algorithms for nonlinear scalar equations. Among these algorithms, the second one is optimal according to Kung-Traub’s conjecture. It is established that the newly proposed algorithms bear the fourth- and sixth-order of convergence. To show the effectiveness of the suggested methods, we provide several real-life problems associated with engineering sciences. These problems have been solved through the suggested methods, and their numerical results proved the superiority of these methods over the other ones. Finally, we study the dynamics of the proposed methods using polynomiographs created with the help of a computer program using six cubic-degree polynomials and then give a detailed graphical comparison with similar existing methods which shows the supremacy of the presented iteration schemes with respect to convergence speed and other dynamical aspects. |
| format | Article |
| id | doaj-art-791ec6c8641645c48ef2b5abe738c5c7 |
| institution | Kabale University |
| issn | 1099-0526 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-791ec6c8641645c48ef2b5abe738c5c72025-02-03T06:13:01ZengWileyComplexity1099-05262022-01-01202210.1155/2022/9705690Optimal Algorithms for Nonlinear Equations with Applications and Their DynamicsAmir Naseem0M. A. Rehman1Nasr Al Din Ide2Department of MathematicsDepartment of MathematicsDepartment of MathematicsIn the present work, we introduce two novel root-finding algorithms for nonlinear scalar equations. Among these algorithms, the second one is optimal according to Kung-Traub’s conjecture. It is established that the newly proposed algorithms bear the fourth- and sixth-order of convergence. To show the effectiveness of the suggested methods, we provide several real-life problems associated with engineering sciences. These problems have been solved through the suggested methods, and their numerical results proved the superiority of these methods over the other ones. Finally, we study the dynamics of the proposed methods using polynomiographs created with the help of a computer program using six cubic-degree polynomials and then give a detailed graphical comparison with similar existing methods which shows the supremacy of the presented iteration schemes with respect to convergence speed and other dynamical aspects.http://dx.doi.org/10.1155/2022/9705690 |
| spellingShingle | Amir Naseem M. A. Rehman Nasr Al Din Ide Optimal Algorithms for Nonlinear Equations with Applications and Their Dynamics Complexity |
| title | Optimal Algorithms for Nonlinear Equations with Applications and Their Dynamics |
| title_full | Optimal Algorithms for Nonlinear Equations with Applications and Their Dynamics |
| title_fullStr | Optimal Algorithms for Nonlinear Equations with Applications and Their Dynamics |
| title_full_unstemmed | Optimal Algorithms for Nonlinear Equations with Applications and Their Dynamics |
| title_short | Optimal Algorithms for Nonlinear Equations with Applications and Their Dynamics |
| title_sort | optimal algorithms for nonlinear equations with applications and their dynamics |
| url | http://dx.doi.org/10.1155/2022/9705690 |
| work_keys_str_mv | AT amirnaseem optimalalgorithmsfornonlinearequationswithapplicationsandtheirdynamics AT marehman optimalalgorithmsfornonlinearequationswithapplicationsandtheirdynamics AT nasraldinide optimalalgorithmsfornonlinearequationswithapplicationsandtheirdynamics |