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...

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Main Authors: Kasmita Devi, Prashanth Maroju
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
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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.
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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