A Family of Optimal Eighth Order Iteration Functions for Multiple Roots and Its Dynamics
In this manuscript, we present a new general family of optimal iterative methods for finding multiple roots of nonlinear equations with known multiplicity using weight functions. An extensive convergence analysis is presented to verify the optimal eighth order convergence of the new family. Some spe...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/5597186 |
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| _version_ | 1832554026588176384 |
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| author | Saima Akram Faiza Akram Moin-ud-Din Junjua Misbah Arshad Tariq Afzal |
| author_facet | Saima Akram Faiza Akram Moin-ud-Din Junjua Misbah Arshad Tariq Afzal |
| author_sort | Saima Akram |
| collection | DOAJ |
| description | In this manuscript, we present a new general family of optimal iterative methods for finding multiple roots of nonlinear equations with known multiplicity using weight functions. An extensive convergence analysis is presented to verify the optimal eighth order convergence of the new family. Some special cases of the family are also presented which require only three functions and one derivative evaluation at each iteration to reach optimal eighth order convergence. A variety of numerical test functions along with some real-world problems such as beam designing model and Van der Waals’ equation of state are presented to ensure that the newly developed family efficiently competes with the other existing methods. The dynamical analysis of the proposed methods is also presented to validate the theoretical results by using graphical tools, termed as the basins of attraction. |
| format | Article |
| id | doaj-art-929681206cc244cabc4b1421ca47957c |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-929681206cc244cabc4b1421ca47957c2025-02-03T05:52:39ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/55971865597186A Family of Optimal Eighth Order Iteration Functions for Multiple Roots and Its DynamicsSaima Akram0Faiza Akram1Moin-ud-Din Junjua2Misbah Arshad3Tariq Afzal4Centre for Advanced Studies in Pure & Applied Mathematics, Bahauddin Zakariya University Multan, Multan 60000, PakistanCentre for Advanced Studies in Pure & Applied Mathematics, Bahauddin Zakariya University Multan, Multan 60000, PakistanDepartment of Mathematics and Statistics, Institute of Southern Punjab Multan, Multan 60000, PakistanDepartment of Mathematics, COMSATS University Islamabad, Sahiwal Campus, Punjab 57000, PakistanDepartment of Mathematics and Statistics, Institute of Southern Punjab Multan, Multan 60000, PakistanIn this manuscript, we present a new general family of optimal iterative methods for finding multiple roots of nonlinear equations with known multiplicity using weight functions. An extensive convergence analysis is presented to verify the optimal eighth order convergence of the new family. Some special cases of the family are also presented which require only three functions and one derivative evaluation at each iteration to reach optimal eighth order convergence. A variety of numerical test functions along with some real-world problems such as beam designing model and Van der Waals’ equation of state are presented to ensure that the newly developed family efficiently competes with the other existing methods. The dynamical analysis of the proposed methods is also presented to validate the theoretical results by using graphical tools, termed as the basins of attraction.http://dx.doi.org/10.1155/2021/5597186 |
| spellingShingle | Saima Akram Faiza Akram Moin-ud-Din Junjua Misbah Arshad Tariq Afzal A Family of Optimal Eighth Order Iteration Functions for Multiple Roots and Its Dynamics Journal of Mathematics |
| title | A Family of Optimal Eighth Order Iteration Functions for Multiple Roots and Its Dynamics |
| title_full | A Family of Optimal Eighth Order Iteration Functions for Multiple Roots and Its Dynamics |
| title_fullStr | A Family of Optimal Eighth Order Iteration Functions for Multiple Roots and Its Dynamics |
| title_full_unstemmed | A Family of Optimal Eighth Order Iteration Functions for Multiple Roots and Its Dynamics |
| title_short | A Family of Optimal Eighth Order Iteration Functions for Multiple Roots and Its Dynamics |
| title_sort | family of optimal eighth order iteration functions for multiple roots and its dynamics |
| url | http://dx.doi.org/10.1155/2021/5597186 |
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