Inverse Family of Numerical Methods for Approximating All Simple and Roots with Multiplicity of Nonlinear Polynomial Equations with Engineering Applications

Shams, M; Rafiq, N; Kausar, N; Ahmed, SF; Mir, NA; Saha, SC

Inverse Family of Numerical Methods for Approximating All Simple and Roots with Multiplicity of Nonlinear Polynomial Equations with Engineering Applications

Shams, M Rafiq, N Kausar, N Ahmed, SF Mir, NA Saha, SC

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Publisher:: Hindawi Limited
Publication Type:: Journal Article
Citation:: Mathematical Problems in Engineering, 2021, 2021, pp. 1-9
Issue Date:: 2021-12-24

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Field	Value	Language
dc.contributor.author	Shams, M
dc.contributor.author	Rafiq, N
dc.contributor.author	Kausar, N
dc.contributor.author	Ahmed, SF
dc.contributor.author	Mir, NA
dc.contributor.author	Saha, SC
dc.date.accessioned	2022-01-12T04:51:33Z
dc.date.available	2022-01-12T04:51:33Z
dc.date.issued	2021-12-24
dc.identifier.citation	Mathematical Problems in Engineering, 2021, 2021, pp. 1-9
dc.identifier.issn	1024-123X
dc.identifier.issn	1563-5147
dc.identifier.uri	http://hdl.handle.net/10453/152974
dc.description.abstract	<jats:p>A new inverse family of the iterative method is interrogated in the present article for simultaneously estimating all distinct and multiple roots of nonlinear polynomial equations. Convergence analysis proves that the order of convergence of the newly constructed family of methods is two. The computer algebra systems CAS-Mathematica is used to determine the lower bound of convergence order, which justifies the local convergence of the newly developed method. Some nonlinear models from physics, chemistry, and engineering sciences are considered to demonstrate the performance and efficiency of the newly constructed family of inverse simultaneous methods in comparison to classical methods in the literature. The computational time in seconds and residual error graph of the inverse simultaneous methods are also presented to elaborate their convergence behavior.</jats:p>
dc.language	en
dc.publisher	Hindawi Limited
dc.relation.ispartof	Mathematical Problems in Engineering
dc.relation.isbasedon	10.1155/2021/3124615
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	01 Mathematical Sciences, 09 Engineering
dc.subject.classification	Numerical & Computational Mathematics
dc.title	Inverse Family of Numerical Methods for Approximating All Simple and Roots with Multiplicity of Nonlinear Polynomial Equations with Engineering Applications
dc.type	Journal Article
utslib.citation.volume	2021
utslib.for	01 Mathematical Sciences
utslib.for	09 Engineering
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Mechanical and Mechatronic Engineering
utslib.copyright.status	open_access	*
dc.date.updated	2022-01-12T04:51:31Z
pubs.publication-status	Published
pubs.volume	2021

Abstract:

A new inverse family of the iterative method is interrogated in the present article for simultaneously estimating all distinct and multiple roots of nonlinear polynomial equations. Convergence analysis proves that the order of convergence of the newly constructed family of methods is two. The computer algebra systems CAS-Mathematica is used to determine the lower bound of convergence order, which justifies the local convergence of the newly developed method. Some nonlinear models from physics, chemistry, and engineering sciences are considered to demonstrate the performance and efficiency of the newly constructed family of inverse simultaneous methods in comparison to classical methods in the literature. The computational time in seconds and residual error graph of the inverse simultaneous methods are also presented to elaborate their convergence behavior.

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http://hdl.handle.net/10453/152974