A novel class of fourth-order derivative-free iterative methods to obtain multiple zeros and their basins of attraction
This article proposed a novel fourth-order class based on weight functions to locate multiple roots numerically, which did not require the evaluation of derivatives at any stage of computation. For particular instances of a multiplicity of zeros, the theoretical convergence behavior of the proposed...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241699 |
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| author | Munish Kansal Vanita Sharma Litika Rani Lorentz Jäntschi |
| author_facet | Munish Kansal Vanita Sharma Litika Rani Lorentz Jäntschi |
| author_sort | Munish Kansal |
| collection | DOAJ |
| description | This article proposed a novel fourth-order class based on weight functions to locate multiple roots numerically, which did not require the evaluation of derivatives at any stage of computation. For particular instances of a multiplicity of zeros, the theoretical convergence behavior of the proposed family has been proven to be symmetrical. This inspired us to show the general results which endorsed the convergence order of the suggested scheme. In addition, some special cases were introduced by using different weight functions. The basins of attraction of the proposed techniques for various parametric values in the complex plane were showcased to verify the stability and convergence features. Finally, we have included a range of problems like Planck's radiation law, the Van der Waals equation, the trajectory of an electron, and a few academic problems. Numerical analyses were performed and compared with other existing algorithms to verify the efficacy and applicability of the proposed techniques. |
| format | Article |
| id | doaj-art-dcd8ef98ccb14c2f8b4d412902ffa955 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-dcd8ef98ccb14c2f8b4d412902ffa9552025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912358233585910.3934/math.20241699A novel class of fourth-order derivative-free iterative methods to obtain multiple zeros and their basins of attractionMunish Kansal0Vanita Sharma1Litika Rani2Lorentz Jäntschi3Department of Mathematics, Thapar Institute of Engineering and Technology, Patiala 147004, IndiaSchool of Commerce, SVKM's Narsee Monjee Institute of Management Studies, Chandigarh 160014, IndiaDepartment of Mathematics, Thapar Institute of Engineering and Technology, Patiala 147004, IndiaDepartment of Physics and Chemistry, Technical University of Cluj-Napoca, Cluj-Napoca 400114, RomaniaThis article proposed a novel fourth-order class based on weight functions to locate multiple roots numerically, which did not require the evaluation of derivatives at any stage of computation. For particular instances of a multiplicity of zeros, the theoretical convergence behavior of the proposed family has been proven to be symmetrical. This inspired us to show the general results which endorsed the convergence order of the suggested scheme. In addition, some special cases were introduced by using different weight functions. The basins of attraction of the proposed techniques for various parametric values in the complex plane were showcased to verify the stability and convergence features. Finally, we have included a range of problems like Planck's radiation law, the Van der Waals equation, the trajectory of an electron, and a few academic problems. Numerical analyses were performed and compared with other existing algorithms to verify the efficacy and applicability of the proposed techniques.https://www.aimspress.com/article/doi/10.3934/math.20241699multiple rootsnonlinear equationsderivative-free methodsbasins of attractionsiterative methods |
| spellingShingle | Munish Kansal Vanita Sharma Litika Rani Lorentz Jäntschi A novel class of fourth-order derivative-free iterative methods to obtain multiple zeros and their basins of attraction AIMS Mathematics multiple roots nonlinear equations derivative-free methods basins of attractions iterative methods |
| title | A novel class of fourth-order derivative-free iterative methods to obtain multiple zeros and their basins of attraction |
| title_full | A novel class of fourth-order derivative-free iterative methods to obtain multiple zeros and their basins of attraction |
| title_fullStr | A novel class of fourth-order derivative-free iterative methods to obtain multiple zeros and their basins of attraction |
| title_full_unstemmed | A novel class of fourth-order derivative-free iterative methods to obtain multiple zeros and their basins of attraction |
| title_short | A novel class of fourth-order derivative-free iterative methods to obtain multiple zeros and their basins of attraction |
| title_sort | novel class of fourth order derivative free iterative methods to obtain multiple zeros and their basins of attraction |
| topic | multiple roots nonlinear equations derivative-free methods basins of attractions iterative methods |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241699 |
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