A Study of Convergence of Sixth-Order Contraharmonic-Mean Newton’s Method (CHN) with Applications and Dynamics
We develop the local convergence of the six order Contraharmonic-mean Newton’s method (CHN) to solve Banach space valued equations. Our analysis approach is two fold: The first way uses Taylor’s series and derivatives of higher orders. The second one uses only the first derivatives. We examine the t...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-01-01
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| Series: | Foundations |
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| Online Access: | https://www.mdpi.com/2673-9321/4/1/5 |
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| author | Manoj K. Singh Ioannis K. Argyros Samundra Regmi |
| author_facet | Manoj K. Singh Ioannis K. Argyros Samundra Regmi |
| author_sort | Manoj K. Singh |
| collection | DOAJ |
| description | We develop the local convergence of the six order Contraharmonic-mean Newton’s method (CHN) to solve Banach space valued equations. Our analysis approach is two fold: The first way uses Taylor’s series and derivatives of higher orders. The second one uses only the first derivatives. We examine the theoretical results by solving a boundary value problem also using the examples relating the proposed method with other’s methods such as Newton’s, Kou’s and Jarratt’s to show that the proposed method performs better. The conjugate maps for second-degree polynomial are verified. We also calculate the fixed points (extraneous). The article is completed with the study of basins of attraction, which support and further validate the theoretical and numerical results. |
| first_indexed | 2024-04-24T18:15:50Z |
| format | Article |
| id | doaj.art-76d0e647cc914636abec88f78f89dfae |
| institution | Directory Open Access Journal |
| issn | 2673-9321 |
| language | English |
| last_indexed | 2024-04-24T18:15:50Z |
| publishDate | 2024-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Foundations |
| spelling | doaj.art-76d0e647cc914636abec88f78f89dfae2024-03-27T13:41:59ZengMDPI AGFoundations2673-93212024-01-0141476010.3390/foundations4010005A Study of Convergence of Sixth-Order Contraharmonic-Mean Newton’s Method (CHN) with Applications and DynamicsManoj K. Singh0Ioannis K. Argyros1Samundra Regmi2Mangalmay Institute of Engineering and Technology, Plot No. 8, Knowledge Park II, Greater Noida 201310, IndiaDepartment of Computing and Mathematical Sciences, Cameron University, Lawton, OK 73505, USADepartment of Mathematics, University of Houston, Houston, TX 77204, USAWe develop the local convergence of the six order Contraharmonic-mean Newton’s method (CHN) to solve Banach space valued equations. Our analysis approach is two fold: The first way uses Taylor’s series and derivatives of higher orders. The second one uses only the first derivatives. We examine the theoretical results by solving a boundary value problem also using the examples relating the proposed method with other’s methods such as Newton’s, Kou’s and Jarratt’s to show that the proposed method performs better. The conjugate maps for second-degree polynomial are verified. We also calculate the fixed points (extraneous). The article is completed with the study of basins of attraction, which support and further validate the theoretical and numerical results.https://www.mdpi.com/2673-9321/4/1/5Newton’s methodlocal convergenceconvergence orderfractalbasins of attraction |
| spellingShingle | Manoj K. Singh Ioannis K. Argyros Samundra Regmi A Study of Convergence of Sixth-Order Contraharmonic-Mean Newton’s Method (CHN) with Applications and Dynamics Foundations Newton’s method local convergence convergence order fractal basins of attraction |
| title | A Study of Convergence of Sixth-Order Contraharmonic-Mean Newton’s Method (CHN) with Applications and Dynamics |
| title_full | A Study of Convergence of Sixth-Order Contraharmonic-Mean Newton’s Method (CHN) with Applications and Dynamics |
| title_fullStr | A Study of Convergence of Sixth-Order Contraharmonic-Mean Newton’s Method (CHN) with Applications and Dynamics |
| title_full_unstemmed | A Study of Convergence of Sixth-Order Contraharmonic-Mean Newton’s Method (CHN) with Applications and Dynamics |
| title_short | A Study of Convergence of Sixth-Order Contraharmonic-Mean Newton’s Method (CHN) with Applications and Dynamics |
| title_sort | study of convergence of sixth order contraharmonic mean newton s method chn with applications and dynamics |
| topic | Newton’s method local convergence convergence order fractal basins of attraction |
| url | https://www.mdpi.com/2673-9321/4/1/5 |
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