Development of Optimal Iterative Methods with Their Applications and Basins of Attraction
In this paper, we construct variants of Bawazir’s iterative methods for solving nonlinear equations having simple roots. The proposed methods are two-step and three-step methods, with and without memory. The Newton method, weight function and divided differences are used to develop the optimal fourt...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-09-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/14/10/2020 |
| _version_ | 1797469822912561152 |
|---|---|
| author | Waikhom Henarita Chanu Sunil Panday G. Thangkhenpau |
| author_facet | Waikhom Henarita Chanu Sunil Panday G. Thangkhenpau |
| author_sort | Waikhom Henarita Chanu |
| collection | DOAJ |
| description | In this paper, we construct variants of Bawazir’s iterative methods for solving nonlinear equations having simple roots. The proposed methods are two-step and three-step methods, with and without memory. The Newton method, weight function and divided differences are used to develop the optimal fourth- and eighth-order without-memory methods while the methods with memory are derivative-free and use two accelerating parameters to increase the order of convergence without any additional function evaluations. The methods without memory satisfy the Kung–Traub conjecture. The convergence properties of the proposed methods are thoroughly investigated using the main theorems that demonstrate the convergence order. We demonstrate the convergence speed of the introduced methods as compared with existing methods by applying the methods to various nonlinear functions and engineering problems. Numerical comparisons specify that the proposed methods are efficient and give tough competition to some well known existing methods. |
| first_indexed | 2024-03-09T19:26:31Z |
| format | Article |
| id | doaj.art-1527505b41e0438cb1b8da0bb1185ad2 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T19:26:31Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-1527505b41e0438cb1b8da0bb1185ad22023-11-24T02:50:49ZengMDPI AGSymmetry2073-89942022-09-011410202010.3390/sym14102020Development of Optimal Iterative Methods with Their Applications and Basins of AttractionWaikhom Henarita Chanu0Sunil Panday1G. Thangkhenpau2Department of Mathematics, National Institute of Technology Manipur, Langol, Imphal 795004, IndiaDepartment of Mathematics, National Institute of Technology Manipur, Langol, Imphal 795004, IndiaDepartment of Mathematics, National Institute of Technology Manipur, Langol, Imphal 795004, IndiaIn this paper, we construct variants of Bawazir’s iterative methods for solving nonlinear equations having simple roots. The proposed methods are two-step and three-step methods, with and without memory. The Newton method, weight function and divided differences are used to develop the optimal fourth- and eighth-order without-memory methods while the methods with memory are derivative-free and use two accelerating parameters to increase the order of convergence without any additional function evaluations. The methods without memory satisfy the Kung–Traub conjecture. The convergence properties of the proposed methods are thoroughly investigated using the main theorems that demonstrate the convergence order. We demonstrate the convergence speed of the introduced methods as compared with existing methods by applying the methods to various nonlinear functions and engineering problems. Numerical comparisons specify that the proposed methods are efficient and give tough competition to some well known existing methods.https://www.mdpi.com/2073-8994/14/10/2020simple rootsnonlinear equationiterative methodserror |
| spellingShingle | Waikhom Henarita Chanu Sunil Panday G. Thangkhenpau Development of Optimal Iterative Methods with Their Applications and Basins of Attraction Symmetry simple roots nonlinear equation iterative methods error |
| title | Development of Optimal Iterative Methods with Their Applications and Basins of Attraction |
| title_full | Development of Optimal Iterative Methods with Their Applications and Basins of Attraction |
| title_fullStr | Development of Optimal Iterative Methods with Their Applications and Basins of Attraction |
| title_full_unstemmed | Development of Optimal Iterative Methods with Their Applications and Basins of Attraction |
| title_short | Development of Optimal Iterative Methods with Their Applications and Basins of Attraction |
| title_sort | development of optimal iterative methods with their applications and basins of attraction |
| topic | simple roots nonlinear equation iterative methods error |
| url | https://www.mdpi.com/2073-8994/14/10/2020 |
| work_keys_str_mv | AT waikhomhenaritachanu developmentofoptimaliterativemethodswiththeirapplicationsandbasinsofattraction AT sunilpanday developmentofoptimaliterativemethodswiththeirapplicationsandbasinsofattraction AT gthangkhenpau developmentofoptimaliterativemethodswiththeirapplicationsandbasinsofattraction |