Complete study of local convergence and basin of attraction of sixth-order iterative method
The local convergence analysis of the parameter based sixth-order iterative method is the primary focus of this article. This investigation was conducted based on the Fréchet derivative of the first order that satisfies the Lipschitz continuity condition. In addition, we developed a conceptual radiu...
Main Authors: | , |
---|---|
Format: | Article |
Language: | English |
Published: |
AIMS Press
2023-07-01
|
Series: | AIMS Mathematics |
Subjects: | |
Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231080?viewType=HTML |
_version_ | 1797778471873675264 |
---|---|
author | Kasmita Devi Prashanth Maroju |
author_facet | Kasmita Devi Prashanth Maroju |
author_sort | Kasmita Devi |
collection | DOAJ |
description | The local convergence analysis of the parameter based sixth-order iterative method is the primary focus of this article. This investigation was conducted based on the Fréchet derivative of the first order that satisfies the Lipschitz continuity condition. In addition, we developed a conceptual radius of convergence for these methods. Also, we discussed the solution behavior of complex polynomials with the basin of attraction. Finally, some numerical examples are provided to illustrate how the conclusions we got can be employed to determine the iterative approach's radius of convergence ball in the context of solving nonlinear equations. We compare the numerical results with our method and the existing sixth order methods proposed by Argyros et al. We observe that using our method yields significantly larger balls than those that already exist. |
first_indexed | 2024-03-12T23:17:47Z |
format | Article |
id | doaj.art-d78606d3ff034696901dd59674d946e1 |
institution | Directory Open Access Journal |
issn | 2473-6988 |
language | English |
last_indexed | 2024-03-12T23:17:47Z |
publishDate | 2023-07-01 |
publisher | AIMS Press |
record_format | Article |
series | AIMS Mathematics |
spelling | doaj.art-d78606d3ff034696901dd59674d946e12023-07-17T01:35:48ZengAIMS PressAIMS Mathematics2473-69882023-07-0189211912120710.3934/math.20231080Complete study of local convergence and basin of attraction of sixth-order iterative methodKasmita Devi0Prashanth Maroju1Department of Mathematics, SAS, VIT-AP University, Amaravati 522237, Andhra Pradesh, IndiaDepartment of Mathematics, SAS, VIT-AP University, Amaravati 522237, Andhra Pradesh, IndiaThe local convergence analysis of the parameter based sixth-order iterative method is the primary focus of this article. This investigation was conducted based on the Fréchet derivative of the first order that satisfies the Lipschitz continuity condition. In addition, we developed a conceptual radius of convergence for these methods. Also, we discussed the solution behavior of complex polynomials with the basin of attraction. Finally, some numerical examples are provided to illustrate how the conclusions we got can be employed to determine the iterative approach's radius of convergence ball in the context of solving nonlinear equations. We compare the numerical results with our method and the existing sixth order methods proposed by Argyros et al. We observe that using our method yields significantly larger balls than those that already exist.https://www.aimspress.com/article/doi/10.3934/math.20231080?viewType=HTMLlocal convergencebasin of attractionnonlinear equationslipschitz continuity conditionfréchet derivative |
spellingShingle | Kasmita Devi Prashanth Maroju Complete study of local convergence and basin of attraction of sixth-order iterative method AIMS Mathematics local convergence basin of attraction nonlinear equations lipschitz continuity condition fréchet derivative |
title | Complete study of local convergence and basin of attraction of sixth-order iterative method |
title_full | Complete study of local convergence and basin of attraction of sixth-order iterative method |
title_fullStr | Complete study of local convergence and basin of attraction of sixth-order iterative method |
title_full_unstemmed | Complete study of local convergence and basin of attraction of sixth-order iterative method |
title_short | Complete study of local convergence and basin of attraction of sixth-order iterative method |
title_sort | complete study of local convergence and basin of attraction of sixth order iterative method |
topic | local convergence basin of attraction nonlinear equations lipschitz continuity condition fréchet derivative |
url | https://www.aimspress.com/article/doi/10.3934/math.20231080?viewType=HTML |
work_keys_str_mv | AT kasmitadevi completestudyoflocalconvergenceandbasinofattractionofsixthorderiterativemethod AT prashanthmaroju completestudyoflocalconvergenceandbasinofattractionofsixthorderiterativemethod |