A Family of Fifth and Sixth Convergence Order Methods for Nonlinear Models
We study the local convergence of a family of fifth and sixth convergence order derivative free methods for solving Banach space valued nonlinear models. Earlier results used hypotheses up to the seventh derivative to show convergence. However, we only use the first divided difference of order one a...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-04-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/4/715 |
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| author | Ioannis K. Argyros Debasis Sharma Christopher I. Argyros Sanjaya Kumar Parhi Shanta Kumari Sunanda |
| author_facet | Ioannis K. Argyros Debasis Sharma Christopher I. Argyros Sanjaya Kumar Parhi Shanta Kumari Sunanda |
| author_sort | Ioannis K. Argyros |
| collection | DOAJ |
| description | We study the local convergence of a family of fifth and sixth convergence order derivative free methods for solving Banach space valued nonlinear models. Earlier results used hypotheses up to the seventh derivative to show convergence. However, we only use the first divided difference of order one as well as the first derivative in our analysis. We also provide computable radius of convergence, error estimates, and uniqueness of the solution results not given in earlier studies. Hence, we expand the applicability of these methods. The dynamical analysis of the discussed family is also presented. Numerical experiments complete this article. |
| first_indexed | 2024-03-10T12:12:54Z |
| format | Article |
| id | doaj.art-c94bdaece35847bfbcdaf9b498543220 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T12:12:54Z |
| publishDate | 2021-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-c94bdaece35847bfbcdaf9b4985432202023-11-21T16:05:56ZengMDPI AGSymmetry2073-89942021-04-0113471510.3390/sym13040715A Family of Fifth and Sixth Convergence Order Methods for Nonlinear ModelsIoannis K. Argyros0Debasis Sharma1Christopher I. Argyros2Sanjaya Kumar Parhi3Shanta Kumari Sunanda4Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USADepartment of Mathematics, IIIT Bhubaneswar, Odisha 751003, IndiaDepartment of Computer Science, University of Oklahoma, Norman, OK 73071, USADepartment of Mathematics, Fakir Mohan University, Odisha 756020, IndiaDepartment of Mathematics, IIIT Bhubaneswar, Odisha 751003, IndiaWe study the local convergence of a family of fifth and sixth convergence order derivative free methods for solving Banach space valued nonlinear models. Earlier results used hypotheses up to the seventh derivative to show convergence. However, we only use the first divided difference of order one as well as the first derivative in our analysis. We also provide computable radius of convergence, error estimates, and uniqueness of the solution results not given in earlier studies. Hence, we expand the applicability of these methods. The dynamical analysis of the discussed family is also presented. Numerical experiments complete this article.https://www.mdpi.com/2073-8994/13/4/715Banach spaceslocal convergencedivided differencefréchet derivativecomplex dynamics |
| spellingShingle | Ioannis K. Argyros Debasis Sharma Christopher I. Argyros Sanjaya Kumar Parhi Shanta Kumari Sunanda A Family of Fifth and Sixth Convergence Order Methods for Nonlinear Models Symmetry Banach spaces local convergence divided difference fréchet derivative complex dynamics |
| title | A Family of Fifth and Sixth Convergence Order Methods for Nonlinear Models |
| title_full | A Family of Fifth and Sixth Convergence Order Methods for Nonlinear Models |
| title_fullStr | A Family of Fifth and Sixth Convergence Order Methods for Nonlinear Models |
| title_full_unstemmed | A Family of Fifth and Sixth Convergence Order Methods for Nonlinear Models |
| title_short | A Family of Fifth and Sixth Convergence Order Methods for Nonlinear Models |
| title_sort | family of fifth and sixth convergence order methods for nonlinear models |
| topic | Banach spaces local convergence divided difference fréchet derivative complex dynamics |
| url | https://www.mdpi.com/2073-8994/13/4/715 |
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