Generating Optimal Eighth Order Methods for Computing Multiple Roots
There are a few optimal eighth order methods in literature for computing multiple zeros of a nonlinear function. Therefore, in this work our main focus is on developing a new family of optimal eighth order iterative methods for multiple zeros. The applicability of proposed methods is demonstrated on...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/12/1947 |
| _version_ | 1797546758536953856 |
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| author | Deepak Kumar Sunil Kumar Janak Raj Sharma Matteo d’Amore |
| author_facet | Deepak Kumar Sunil Kumar Janak Raj Sharma Matteo d’Amore |
| author_sort | Deepak Kumar |
| collection | DOAJ |
| description | There are a few optimal eighth order methods in literature for computing multiple zeros of a nonlinear function. Therefore, in this work our main focus is on developing a new family of optimal eighth order iterative methods for multiple zeros. The applicability of proposed methods is demonstrated on some real life and academic problems that illustrate the efficient convergence behavior. It is shown that the newly developed schemes are able to compete with other methods in terms of numerical error, convergence and computational time. Stability is also demonstrated by means of a pictorial tool, namely, basins of attraction that have the fractal-like shapes along the borders through which basins are symmetric. |
| first_indexed | 2024-03-10T14:34:41Z |
| format | Article |
| id | doaj.art-2a4f1ee24796414291e7ee8913c3a325 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T14:34:41Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-2a4f1ee24796414291e7ee8913c3a3252023-11-20T22:18:21ZengMDPI AGSymmetry2073-89942020-11-011212194710.3390/sym12121947Generating Optimal Eighth Order Methods for Computing Multiple RootsDeepak Kumar0Sunil Kumar1Janak Raj Sharma2Matteo d’Amore3Department of Mathematics, Chandigarh University, Gharuan, Mohali 140413, IndiaDepartment of Mathematics, Sant Longowal Institute of Engineering and Technology Longowal, Sangrur 148106, IndiaDepartment of Mathematics, Sant Longowal Institute of Engineering and Technology Longowal, Sangrur 148106, IndiaDifarma, University of Salerno, Via Giovanni II, 132, 84084 Fisciano (SA), ItalyThere are a few optimal eighth order methods in literature for computing multiple zeros of a nonlinear function. Therefore, in this work our main focus is on developing a new family of optimal eighth order iterative methods for multiple zeros. The applicability of proposed methods is demonstrated on some real life and academic problems that illustrate the efficient convergence behavior. It is shown that the newly developed schemes are able to compete with other methods in terms of numerical error, convergence and computational time. Stability is also demonstrated by means of a pictorial tool, namely, basins of attraction that have the fractal-like shapes along the borders through which basins are symmetric.https://www.mdpi.com/2073-8994/12/12/1947nonlinear equationsNewton methodmultiple rootsoptimal convergence |
| spellingShingle | Deepak Kumar Sunil Kumar Janak Raj Sharma Matteo d’Amore Generating Optimal Eighth Order Methods for Computing Multiple Roots Symmetry nonlinear equations Newton method multiple roots optimal convergence |
| title | Generating Optimal Eighth Order Methods for Computing Multiple Roots |
| title_full | Generating Optimal Eighth Order Methods for Computing Multiple Roots |
| title_fullStr | Generating Optimal Eighth Order Methods for Computing Multiple Roots |
| title_full_unstemmed | Generating Optimal Eighth Order Methods for Computing Multiple Roots |
| title_short | Generating Optimal Eighth Order Methods for Computing Multiple Roots |
| title_sort | generating optimal eighth order methods for computing multiple roots |
| topic | nonlinear equations Newton method multiple roots optimal convergence |
| url | https://www.mdpi.com/2073-8994/12/12/1947 |
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