Higher Order Numerical Approaches for Nonlinear Equations by Decomposition Technique

In this paper, a unique decomposition technique is implemented along with an auxiliary function for the best implementation. Some new and efficient techniques are introduced and analyzed for nonlinear equations. These techniques are higher ordered in approaching to the root of nonlinear equations. S...

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Main Authors:	Abdulghani Ragaa Alharbi, Muhammed Imran Faisal, Farooq Ahmed Shah, Muhammad Waseem, Roman Ullah, Saira Sherbaz
Format:	Article
Language:	English
Published:	IEEE 2019-01-01
Series:	IEEE Access
Subjects:	Decomposition technique iterative scheme convergence analysis newton method numerical examples coupled system of equations
Online Access:	https://ieeexplore.ieee.org/document/8681066/

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spelling	doaj-811169f63aac4e268390027483c4b8e62021-03-29T22:13:53ZengIEEEIEEE Access2169-35362019-01-017443294433710.1109/ACCESS.2019.29064708681066Higher Order Numerical Approaches for Nonlinear Equations by Decomposition TechniqueAbdulghani Ragaa Alharbi0Muhammed Imran Faisal1https://orcid.org/0000-0002-4169-4366Farooq Ahmed Shah2Muhammad Waseem3Roman Ullah4Saira Sherbaz5Department of Mathematics, Faculty of Science, Taibah University, Medina, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Taibah University, Medina, Saudi ArabiaDepartment of Mathematics, Attock Campus, COMSATS University Islamabad, Attock, PakistanDepartment of Mathematics, Vehari Campus, COMSATS University Islamabad, Vehari, PakistanDepartment of Mathematics, Muscat College, Muscat, OmanDepartment of Mathematics, Attock Campus, COMSATS University Islamabad, Attock, PakistanIn this paper, a unique decomposition technique is implemented along with an auxiliary function for the best implementation. Some new and efficient techniques are introduced and analyzed for nonlinear equations. These techniques are higher ordered in approaching to the root of nonlinear equations. Some existing classical methods such as the Newton method, Halley method, and Traub's approach and their various modified forms are the special cases of these newly purposed schemes. These new iterative schemes are a good addition in existing methods and are also a comprehensive and generalized form for finding the solution of nonlinear equations.https://ieeexplore.ieee.org/document/8681066/Decomposition techniqueiterative schemeconvergence analysisnewton methodnumerical examplescoupled system of equations
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Abdulghani Ragaa Alharbi Muhammed Imran Faisal Farooq Ahmed Shah Muhammad Waseem Roman Ullah Saira Sherbaz
spellingShingle	Abdulghani Ragaa Alharbi Muhammed Imran Faisal Farooq Ahmed Shah Muhammad Waseem Roman Ullah Saira Sherbaz Higher Order Numerical Approaches for Nonlinear Equations by Decomposition Technique IEEE Access Decomposition technique iterative scheme convergence analysis newton method numerical examples coupled system of equations
author_facet	Abdulghani Ragaa Alharbi Muhammed Imran Faisal Farooq Ahmed Shah Muhammad Waseem Roman Ullah Saira Sherbaz
author_sort	Abdulghani Ragaa Alharbi
title	Higher Order Numerical Approaches for Nonlinear Equations by Decomposition Technique
title_short	Higher Order Numerical Approaches for Nonlinear Equations by Decomposition Technique
title_full	Higher Order Numerical Approaches for Nonlinear Equations by Decomposition Technique
title_fullStr	Higher Order Numerical Approaches for Nonlinear Equations by Decomposition Technique
title_full_unstemmed	Higher Order Numerical Approaches for Nonlinear Equations by Decomposition Technique
title_sort	higher order numerical approaches for nonlinear equations by decomposition technique
publisher	IEEE
series	IEEE Access
issn	2169-3536
publishDate	2019-01-01
description	In this paper, a unique decomposition technique is implemented along with an auxiliary function for the best implementation. Some new and efficient techniques are introduced and analyzed for nonlinear equations. These techniques are higher ordered in approaching to the root of nonlinear equations. Some existing classical methods such as the Newton method, Halley method, and Traub's approach and their various modified forms are the special cases of these newly purposed schemes. These new iterative schemes are a good addition in existing methods and are also a comprehensive and generalized form for finding the solution of nonlinear equations.
topic	Decomposition technique iterative scheme convergence analysis newton method numerical examples coupled system of equations
url	https://ieeexplore.ieee.org/document/8681066/
work_keys_str_mv	AT abdulghaniragaaalharbi higherordernumericalapproachesfornonlinearequationsbydecompositiontechnique AT muhammedimranfaisal higherordernumericalapproachesfornonlinearequationsbydecompositiontechnique AT farooqahmedshah higherordernumericalapproachesfornonlinearequationsbydecompositiontechnique AT muhammadwaseem higherordernumericalapproachesfornonlinearequationsbydecompositiontechnique AT romanullah higherordernumericalapproachesfornonlinearequationsbydecompositiontechnique AT sairasherbaz higherordernumericalapproachesfornonlinearequationsbydecompositiontechnique
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Higher Order Numerical Approaches for Nonlinear Equations by Decomposition Technique

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