Behind Jarratt’s Steps: Is Jarratt’s Scheme the Best Version of Itself?
In this paper, we analyze the stability of the family of iterative methods designed by Jarratt using complex dynamics tools. This allows us to conclude whether the scheme known as Jarratt’s method is the most stable among all the elements of the family. We deduce that classical Jarratt’s scheme is n...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2023-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2023/8840525 |
| _version_ | 1797797297019420672 |
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| author | Alicia Cordero Elaine Segura Juan R. Torregrosa |
| author_facet | Alicia Cordero Elaine Segura Juan R. Torregrosa |
| author_sort | Alicia Cordero |
| collection | DOAJ |
| description | In this paper, we analyze the stability of the family of iterative methods designed by Jarratt using complex dynamics tools. This allows us to conclude whether the scheme known as Jarratt’s method is the most stable among all the elements of the family. We deduce that classical Jarratt’s scheme is not the only stable element of the family. We also obtain information about the members of the class with chaotical behavior. Some numerical results are presented for confirming the convergence and stability results. |
| first_indexed | 2024-03-13T03:46:03Z |
| format | Article |
| id | doaj.art-dc6dfccbea8044e9a8ac14a90761c00d |
| institution | Directory Open Access Journal |
| issn | 1607-887X |
| language | English |
| last_indexed | 2024-03-13T03:46:03Z |
| publishDate | 2023-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj.art-dc6dfccbea8044e9a8ac14a90761c00d2023-06-23T00:00:02ZengHindawi LimitedDiscrete Dynamics in Nature and Society1607-887X2023-01-01202310.1155/2023/8840525Behind Jarratt’s Steps: Is Jarratt’s Scheme the Best Version of Itself?Alicia Cordero0Elaine Segura1Juan R. Torregrosa2Instituto Universitario de Matemática MultidisciplinarDepartamento de MatemáticaInstituto Universitario de Matemática MultidisciplinarIn this paper, we analyze the stability of the family of iterative methods designed by Jarratt using complex dynamics tools. This allows us to conclude whether the scheme known as Jarratt’s method is the most stable among all the elements of the family. We deduce that classical Jarratt’s scheme is not the only stable element of the family. We also obtain information about the members of the class with chaotical behavior. Some numerical results are presented for confirming the convergence and stability results.http://dx.doi.org/10.1155/2023/8840525 |
| spellingShingle | Alicia Cordero Elaine Segura Juan R. Torregrosa Behind Jarratt’s Steps: Is Jarratt’s Scheme the Best Version of Itself? Discrete Dynamics in Nature and Society |
| title | Behind Jarratt’s Steps: Is Jarratt’s Scheme the Best Version of Itself? |
| title_full | Behind Jarratt’s Steps: Is Jarratt’s Scheme the Best Version of Itself? |
| title_fullStr | Behind Jarratt’s Steps: Is Jarratt’s Scheme the Best Version of Itself? |
| title_full_unstemmed | Behind Jarratt’s Steps: Is Jarratt’s Scheme the Best Version of Itself? |
| title_short | Behind Jarratt’s Steps: Is Jarratt’s Scheme the Best Version of Itself? |
| title_sort | behind jarratt s steps is jarratt s scheme the best version of itself |
| url | http://dx.doi.org/10.1155/2023/8840525 |
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