Inverse Numerical Iterative Technique for Finding all Roots of Nonlinear Equations with Engineering Applications

Inverse Numerical Iterative Technique for Finding all Roots of Nonlinear Equations with Engineering Applications

We introduce here a new two-step derivate-free inverse simultaneous iterative method for estimating all roots of nonlinear equation. It is proved that convergence order of the newly constructed method is four. Lower bound of the convergence order is determined using Mathematica and verified with the...

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Main Authors: Mudassir Shams, Naila Rafiq, Babar Ahmad, Nazir Ahmad Mir
Format: Article
Language:English
Published: Hindawi Limited 2021-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2021/6643514
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spelling doaj-f22cedd3e1754ba385f1f20ecb612fac2021-02-15T12:53:05ZengHindawi LimitedJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/66435146643514Inverse Numerical Iterative Technique for Finding all Roots of Nonlinear Equations with Engineering ApplicationsMudassir Shams0Naila Rafiq1Babar Ahmad2Nazir Ahmad Mir3Department of Mathematics and Statistics, Riphah International University I-14, Islamabad 44000, PakistanDepartment of Mathematics, NUML, Islamabad, PakistanDepartment of Mathematics, Comsats University Islamabad, Islamabad 44000, PakistanDepartment of Mathematics and Statistics, Riphah International University I-14, Islamabad 44000, PakistanWe introduce here a new two-step derivate-free inverse simultaneous iterative method for estimating all roots of nonlinear equation. It is proved that convergence order of the newly constructed method is four. Lower bound of the convergence order is determined using Mathematica and verified with theoretical local convergence order of the method introduced. Some nonlinear models which are taken from physical and engineering sciences as numerical test examples to demonstrate the performance and efficiency of the newly constructed modified inverse simultaneous methods as compared to classical methods existing in literature are presented. Dynamical planes and residual graphs are drawn using MATLAB to elaborate efficiency, robustness, and authentication in its domain.http://dx.doi.org/10.1155/2021/6643514
collection DOAJ
language English
format Article
sources DOAJ
author Mudassir Shams
Naila Rafiq
Babar Ahmad
Nazir Ahmad Mir
spellingShingle Mudassir Shams
Naila Rafiq
Babar Ahmad
Nazir Ahmad Mir
Inverse Numerical Iterative Technique for Finding all Roots of Nonlinear Equations with Engineering Applications
Journal of Mathematics
author_facet Mudassir Shams
Naila Rafiq
Babar Ahmad
Nazir Ahmad Mir
author_sort Mudassir Shams
title Inverse Numerical Iterative Technique for Finding all Roots of Nonlinear Equations with Engineering Applications
title_short Inverse Numerical Iterative Technique for Finding all Roots of Nonlinear Equations with Engineering Applications
title_full Inverse Numerical Iterative Technique for Finding all Roots of Nonlinear Equations with Engineering Applications
title_fullStr Inverse Numerical Iterative Technique for Finding all Roots of Nonlinear Equations with Engineering Applications
title_full_unstemmed Inverse Numerical Iterative Technique for Finding all Roots of Nonlinear Equations with Engineering Applications
title_sort inverse numerical iterative technique for finding all roots of nonlinear equations with engineering applications
publisher Hindawi Limited
series Journal of Mathematics
issn 2314-4629
2314-4785
publishDate 2021-01-01
description We introduce here a new two-step derivate-free inverse simultaneous iterative method for estimating all roots of nonlinear equation. It is proved that convergence order of the newly constructed method is four. Lower bound of the convergence order is determined using Mathematica and verified with theoretical local convergence order of the method introduced. Some nonlinear models which are taken from physical and engineering sciences as numerical test examples to demonstrate the performance and efficiency of the newly constructed modified inverse simultaneous methods as compared to classical methods existing in literature are presented. Dynamical planes and residual graphs are drawn using MATLAB to elaborate efficiency, robustness, and authentication in its domain.
url http://dx.doi.org/10.1155/2021/6643514
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AT nailarafiq inversenumericaliterativetechniqueforfindingallrootsofnonlinearequationswithengineeringapplications
AT babarahmad inversenumericaliterativetechniqueforfindingallrootsofnonlinearequationswithengineeringapplications
AT nazirahmadmir inversenumericaliterativetechniqueforfindingallrootsofnonlinearequationswithengineeringapplications
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