On iterative techniques for estimating all roots of nonlinear equation and its system with application in differential equation

Abstract In this article, we construct a family of iterative methods for finding a single root of nonlinear equation and then generalize this family of iterative methods for determining all roots of nonlinear equations simultaneously. Further we extend this family of root estimating methods for solv...

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Autores principales:	Mudassir Shams, Naila Rafiq, Nasreen Kausar, Praveen Agarwal, Choonkil Park, Nazir Ahmad Mir
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2021
Materias:	Single and all roots Nonlinear system of equations Iterative methods Simultaneous methods Basins of attraction Boundary value problems Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/081d02c546064937a35523502a0f6da3
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id	oai:doaj.org-article:081d02c546064937a35523502a0f6da3
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spelling	oai:doaj.org-article:081d02c546064937a35523502a0f6da32021-11-07T12:13:14ZOn iterative techniques for estimating all roots of nonlinear equation and its system with application in differential equation10.1186/s13662-021-03636-x1687-1847https://doaj.org/article/081d02c546064937a35523502a0f6da32021-11-01T00:00:00Zhttps://doi.org/10.1186/s13662-021-03636-xhttps://doaj.org/toc/1687-1847Abstract In this article, we construct a family of iterative methods for finding a single root of nonlinear equation and then generalize this family of iterative methods for determining all roots of nonlinear equations simultaneously. Further we extend this family of root estimating methods for solving a system of nonlinear equations. Convergence analysis shows that the order of convergence is 3 in case of the single root finding method as well as for the system of nonlinear equations and is 5 for simultaneous determination of all distinct and multiple roots of a nonlinear equation. The computational cost, basin of attraction, efficiency, log of residual and numerical test examples show that the newly constructed methods are more efficient as compared to the existing methods in literature.Mudassir ShamsNaila RafiqNasreen KausarPraveen AgarwalChoonkil ParkNazir Ahmad MirSpringerOpenarticleSingle and all rootsNonlinear system of equationsIterative methodsSimultaneous methodsBasins of attractionBoundary value problemsMathematicsQA1-939ENAdvances in Difference Equations, Vol 2021, Iss 1, Pp 1-18 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Single and all roots Nonlinear system of equations Iterative methods Simultaneous methods Basins of attraction Boundary value problems Mathematics QA1-939
spellingShingle	Single and all roots Nonlinear system of equations Iterative methods Simultaneous methods Basins of attraction Boundary value problems Mathematics QA1-939 Mudassir Shams Naila Rafiq Nasreen Kausar Praveen Agarwal Choonkil Park Nazir Ahmad Mir On iterative techniques for estimating all roots of nonlinear equation and its system with application in differential equation
description	Abstract In this article, we construct a family of iterative methods for finding a single root of nonlinear equation and then generalize this family of iterative methods for determining all roots of nonlinear equations simultaneously. Further we extend this family of root estimating methods for solving a system of nonlinear equations. Convergence analysis shows that the order of convergence is 3 in case of the single root finding method as well as for the system of nonlinear equations and is 5 for simultaneous determination of all distinct and multiple roots of a nonlinear equation. The computational cost, basin of attraction, efficiency, log of residual and numerical test examples show that the newly constructed methods are more efficient as compared to the existing methods in literature.
format	article
author	Mudassir Shams Naila Rafiq Nasreen Kausar Praveen Agarwal Choonkil Park Nazir Ahmad Mir
author_facet	Mudassir Shams Naila Rafiq Nasreen Kausar Praveen Agarwal Choonkil Park Nazir Ahmad Mir
author_sort	Mudassir Shams
title	On iterative techniques for estimating all roots of nonlinear equation and its system with application in differential equation
title_short	On iterative techniques for estimating all roots of nonlinear equation and its system with application in differential equation
title_full	On iterative techniques for estimating all roots of nonlinear equation and its system with application in differential equation
title_fullStr	On iterative techniques for estimating all roots of nonlinear equation and its system with application in differential equation
title_full_unstemmed	On iterative techniques for estimating all roots of nonlinear equation and its system with application in differential equation
title_sort	on iterative techniques for estimating all roots of nonlinear equation and its system with application in differential equation
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/081d02c546064937a35523502a0f6da3
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On iterative techniques for estimating all roots of nonlinear equation and its system with application in differential equation

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