New Iterative Schemes to Solve Nonlinear Systems with Symmetric Basins of Attraction
We present a new Jarratt-type family of optimal fourth- and sixth-order iterative methods for solving nonlinear equations, along with their convergence properties. The schemes are extended to nonlinear systems of equations with equal convergence order. The stability properties of the vectorial schem...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-08-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/8/1742 |
| _version_ | 1797407707839332352 |
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| author | Alicia Cordero Smmayya Iqbal Juan R. Torregrosa Fiza Zafar |
| author_facet | Alicia Cordero Smmayya Iqbal Juan R. Torregrosa Fiza Zafar |
| author_sort | Alicia Cordero |
| collection | DOAJ |
| description | We present a new Jarratt-type family of optimal fourth- and sixth-order iterative methods for solving nonlinear equations, along with their convergence properties. The schemes are extended to nonlinear systems of equations with equal convergence order. The stability properties of the vectorial schemes are analyzed, showing their symmetric wide sets of converging initial guesses. To illustrate the applicability of our methods for the multidimensional case, we choose some real world problems such as kinematic syntheses, boundary value problems, Fisher’s and Hammerstein’s integrals, etc. Numerical comparisons are given to show the performance of our schemes, compared with the existing efficient methods. |
| first_indexed | 2024-03-09T03:46:29Z |
| format | Article |
| id | doaj.art-7110cd3496bf468ab31f31881758b49a |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T03:46:29Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-7110cd3496bf468ab31f31881758b49a2023-12-03T14:33:59ZengMDPI AGSymmetry2073-89942022-08-01148174210.3390/sym14081742New Iterative Schemes to Solve Nonlinear Systems with Symmetric Basins of AttractionAlicia Cordero0Smmayya Iqbal1Juan R. Torregrosa2Fiza Zafar3Multidisciplinary Mathematics Institute, Universitat Politècnica de Valenència, Camino de Vera s/n, 46022 València, SpainCentre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, PakistanMultidisciplinary Mathematics Institute, Universitat Politècnica de Valenència, Camino de Vera s/n, 46022 València, SpainCentre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, PakistanWe present a new Jarratt-type family of optimal fourth- and sixth-order iterative methods for solving nonlinear equations, along with their convergence properties. The schemes are extended to nonlinear systems of equations with equal convergence order. The stability properties of the vectorial schemes are analyzed, showing their symmetric wide sets of converging initial guesses. To illustrate the applicability of our methods for the multidimensional case, we choose some real world problems such as kinematic syntheses, boundary value problems, Fisher’s and Hammerstein’s integrals, etc. Numerical comparisons are given to show the performance of our schemes, compared with the existing efficient methods.https://www.mdpi.com/2073-8994/14/8/1742nonlinear systemsiterative methodsstability analysissymmetric basins of attraction |
| spellingShingle | Alicia Cordero Smmayya Iqbal Juan R. Torregrosa Fiza Zafar New Iterative Schemes to Solve Nonlinear Systems with Symmetric Basins of Attraction Symmetry nonlinear systems iterative methods stability analysis symmetric basins of attraction |
| title | New Iterative Schemes to Solve Nonlinear Systems with Symmetric Basins of Attraction |
| title_full | New Iterative Schemes to Solve Nonlinear Systems with Symmetric Basins of Attraction |
| title_fullStr | New Iterative Schemes to Solve Nonlinear Systems with Symmetric Basins of Attraction |
| title_full_unstemmed | New Iterative Schemes to Solve Nonlinear Systems with Symmetric Basins of Attraction |
| title_short | New Iterative Schemes to Solve Nonlinear Systems with Symmetric Basins of Attraction |
| title_sort | new iterative schemes to solve nonlinear systems with symmetric basins of attraction |
| topic | nonlinear systems iterative methods stability analysis symmetric basins of attraction |
| url | https://www.mdpi.com/2073-8994/14/8/1742 |
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