A family of optimal eighth order iteration functions for multiple roots and its dynamics
type: Item
instance of: scholarly article
title: A family of optimal eighth order iteration functions for multiple roots and its dynamics
zbMATH Open document ID: 1477.65074
DOI: 10.1155/2021/5597186
author: Saima Akram
author: Faiza Akram
author: Moin-ud-Din Junjua
author: Misbah Arshad
author: Tariq Afzal
published in: Journal of Mathematics
publication date: 2021-06-22T00:00:00Z
review text: Summary: In this manuscript, we present a new general family of optimal iterative methods for finding multiple roots of nonlinear equations with known multiplicity using weight functions. An extensive convergence analysis is presented to verify the optimal eighth order convergence of the new family. Some special cases of the family are also presented which require only three functions and one derivative evaluation at each iteration to reach optimal eighth order convergence. A variety of numerical test functions along with some real-world problems such as beam designing model and Van der Waals' equation of state are presented to ensure that the newly developed family efficiently competes with the other existing methods. The dynamical analysis of the proposed methods is also presented to validate the theoretical results by using graphical tools, termed as the basins of attraction.
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 7362005
describes a project that uses: Maple
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/5597186
OpenAlex ID: W3136289413
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description: scientific article; zbMATH DE number 7362005