Semilocal convergence analysis of an eighth order iterative method for solving nonlinear systems
In this paper, the semilocal convergence of the eighth order iterative method is proved in Banach space by using the recursive relation, and the proof process does not need high order derivative. By selecting the appropriate initial point and applying the Lipschitz condition to the first order Fréch...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-07-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231141?viewType=HTML |
| _version_ | 1797768350847205376 |
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| author | Xiaofeng Wang Yufan Yang Yuping Qin |
| author_facet | Xiaofeng Wang Yufan Yang Yuping Qin |
| author_sort | Xiaofeng Wang |
| collection | DOAJ |
| description | In this paper, the semilocal convergence of the eighth order iterative method is proved in Banach space by using the recursive relation, and the proof process does not need high order derivative. By selecting the appropriate initial point and applying the Lipschitz condition to the first order Fréchet derivative in the whole region, the existence and uniqueness domain are obtained. In addition, the theoretical results of semilocal convergence are applied to two nonlinear systems, and satisfactory results are obtained. |
| first_indexed | 2024-03-12T20:52:11Z |
| format | Article |
| id | doaj.art-72e66b7f09304aa38d53461959372f90 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-12T20:52:11Z |
| publishDate | 2023-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-72e66b7f09304aa38d53461959372f902023-08-01T01:10:08ZengAIMS PressAIMS Mathematics2473-69882023-07-0189223712238410.3934/math.20231141Semilocal convergence analysis of an eighth order iterative method for solving nonlinear systemsXiaofeng Wang0Yufan Yang1Yuping Qin2School of Mathematical Sciences, Bohai University, Jinzhou 121000, ChinaSchool of Mathematical Sciences, Bohai University, Jinzhou 121000, ChinaSchool of Mathematical Sciences, Bohai University, Jinzhou 121000, ChinaIn this paper, the semilocal convergence of the eighth order iterative method is proved in Banach space by using the recursive relation, and the proof process does not need high order derivative. By selecting the appropriate initial point and applying the Lipschitz condition to the first order Fréchet derivative in the whole region, the existence and uniqueness domain are obtained. In addition, the theoretical results of semilocal convergence are applied to two nonlinear systems, and satisfactory results are obtained.https://www.aimspress.com/article/doi/10.3934/math.20231141?viewType=HTMLnonlinear systemiterative methodrecurrence relationsemilocal convergenceexistence domainunique domain |
| spellingShingle | Xiaofeng Wang Yufan Yang Yuping Qin Semilocal convergence analysis of an eighth order iterative method for solving nonlinear systems AIMS Mathematics nonlinear system iterative method recurrence relation semilocal convergence existence domain unique domain |
| title | Semilocal convergence analysis of an eighth order iterative method for solving nonlinear systems |
| title_full | Semilocal convergence analysis of an eighth order iterative method for solving nonlinear systems |
| title_fullStr | Semilocal convergence analysis of an eighth order iterative method for solving nonlinear systems |
| title_full_unstemmed | Semilocal convergence analysis of an eighth order iterative method for solving nonlinear systems |
| title_short | Semilocal convergence analysis of an eighth order iterative method for solving nonlinear systems |
| title_sort | semilocal convergence analysis of an eighth order iterative method for solving nonlinear systems |
| topic | nonlinear system iterative method recurrence relation semilocal convergence existence domain unique domain |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231141?viewType=HTML |
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