Ball convergence of Potra-Ptak-type method with optimal fourth order of convergence
We present a local convergence analysis Potra-Ptak-type method with optimal fourth order of convergence in order to approximate a solution of a nonlinear equation. In earlier studies such as [1], [5]-[28] hypotheses up to the fourth derivative are used. In this paper we use hypotheses up to the...
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
2021-11-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
| Subjects: | |
| Online Access: | https://www.ictp.acad.ro/jnaat/journal/article/view/1247 |
| _version_ | 1818529604189552640 |
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| author | Ioannis K. Argyros Santhosh George |
| author_facet | Ioannis K. Argyros Santhosh George |
| author_sort | Ioannis K. Argyros |
| collection | DOAJ |
| description |
We present a local convergence analysis Potra-Ptak-type method with optimal fourth order of convergence in order to approximate a solution of a nonlinear equation. In earlier studies such as [1], [5]-[28] hypotheses up to the fourth derivative are used.
In this paper we use hypotheses up to the first derivative only, so that the applicability of these methods is extended under weaker hypotheses. Moreover the radius of convergence and computable error bounds on the distances involved are also given in this study. Numerical examples are also presented in this study.
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| first_indexed | 2024-12-11T17:08:59Z |
| format | Article |
| id | doaj.art-42d9bdbab2ec4c49b4ce2c12d4992c1c |
| institution | Directory Open Access Journal |
| issn | 2457-6794 2501-059X |
| language | English |
| last_indexed | 2024-12-11T17:08:59Z |
| publishDate | 2021-11-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Journal of Numerical Analysis and Approximation Theory |
| spelling | doaj.art-42d9bdbab2ec4c49b4ce2c12d4992c1c2022-12-22T00:57:36ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X2021-11-01501Ball convergence of Potra-Ptak-type method with optimal fourth order of convergenceIoannis K. Argyros0Santhosh George1Cameron UniversityNIT Karnataka We present a local convergence analysis Potra-Ptak-type method with optimal fourth order of convergence in order to approximate a solution of a nonlinear equation. In earlier studies such as [1], [5]-[28] hypotheses up to the fourth derivative are used. In this paper we use hypotheses up to the first derivative only, so that the applicability of these methods is extended under weaker hypotheses. Moreover the radius of convergence and computable error bounds on the distances involved are also given in this study. Numerical examples are also presented in this study. https://www.ictp.acad.ro/jnaat/journal/article/view/1247Potra-Ptak-type methodNewton's methodorder of convergencelocal convergence |
| spellingShingle | Ioannis K. Argyros Santhosh George Ball convergence of Potra-Ptak-type method with optimal fourth order of convergence Journal of Numerical Analysis and Approximation Theory Potra-Ptak-type method Newton's method order of convergence local convergence |
| title | Ball convergence of Potra-Ptak-type method with optimal fourth order of convergence |
| title_full | Ball convergence of Potra-Ptak-type method with optimal fourth order of convergence |
| title_fullStr | Ball convergence of Potra-Ptak-type method with optimal fourth order of convergence |
| title_full_unstemmed | Ball convergence of Potra-Ptak-type method with optimal fourth order of convergence |
| title_short | Ball convergence of Potra-Ptak-type method with optimal fourth order of convergence |
| title_sort | ball convergence of potra ptak type method with optimal fourth order of convergence |
| topic | Potra-Ptak-type method Newton's method order of convergence local convergence |
| url | https://www.ictp.acad.ro/jnaat/journal/article/view/1247 |
| work_keys_str_mv | AT ioanniskargyros ballconvergenceofpotraptaktypemethodwithoptimalfourthorderofconvergence AT santhoshgeorge ballconvergenceofpotraptaktypemethodwithoptimalfourthorderofconvergence |