An Iterative Solver in the Presence and Absence of Multiplicity for Nonlinear Equations

An Iterative Solver in the Presence and Absence of Multiplicity for Nonlinear Equations

We develop a high-order fixed point type method to approximate a multiple root. By using three functional evaluations per full cycle, a new class of fourth-order methods for this purpose is suggested and established. The methods from the class require the knowledge of the multiplicity. We also prese...

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Main Authors: Fazlollah Soleymani, Stanford Shateyi, Gülcan Özkum
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:The Scientific World Journal
Online Access:http://dx.doi.org/10.1155/2013/837243
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spelling doaj-ef6d2c2193214a01ac2b9e9fd1534e9e2020-11-24T21:30:56ZengHindawi LimitedThe Scientific World Journal1537-744X2013-01-01201310.1155/2013/837243837243An Iterative Solver in the Presence and Absence of Multiplicity for Nonlinear EquationsFazlollah Soleymani0Stanford Shateyi1Gülcan Özkum2Young Researchers and Elite Club, Zahedan Branch, Islamic Azad University, Zahedan, IranDepartment of Mathematics, University of Venda, Private Bag X5050, Thohoyandou 0950, South AfricaDepartment of Mathematics, Science and Letter Faculty, Kocaeli University, Umuttepe Campus, Kocaeli, TurkeyWe develop a high-order fixed point type method to approximate a multiple root. By using three functional evaluations per full cycle, a new class of fourth-order methods for this purpose is suggested and established. The methods from the class require the knowledge of the multiplicity. We also present a method in the absence of multiplicity for nonlinear equations. In order to attest the efficiency of the obtained methods, we employ numerical comparisons alongside obtaining basins of attraction to compare them in the complex plane according to their convergence speed and chaotic behavior.http://dx.doi.org/10.1155/2013/837243
collection DOAJ
language English
format Article
sources DOAJ
author Fazlollah Soleymani
Stanford Shateyi
Gülcan Özkum
spellingShingle Fazlollah Soleymani
Stanford Shateyi
Gülcan Özkum
An Iterative Solver in the Presence and Absence of Multiplicity for Nonlinear Equations
The Scientific World Journal
author_facet Fazlollah Soleymani
Stanford Shateyi
Gülcan Özkum
author_sort Fazlollah Soleymani
title An Iterative Solver in the Presence and Absence of Multiplicity for Nonlinear Equations
title_short An Iterative Solver in the Presence and Absence of Multiplicity for Nonlinear Equations
title_full An Iterative Solver in the Presence and Absence of Multiplicity for Nonlinear Equations
title_fullStr An Iterative Solver in the Presence and Absence of Multiplicity for Nonlinear Equations
title_full_unstemmed An Iterative Solver in the Presence and Absence of Multiplicity for Nonlinear Equations
title_sort iterative solver in the presence and absence of multiplicity for nonlinear equations
publisher Hindawi Limited
series The Scientific World Journal
issn 1537-744X
publishDate 2013-01-01
description We develop a high-order fixed point type method to approximate a multiple root. By using three functional evaluations per full cycle, a new class of fourth-order methods for this purpose is suggested and established. The methods from the class require the knowledge of the multiplicity. We also present a method in the absence of multiplicity for nonlinear equations. In order to attest the efficiency of the obtained methods, we employ numerical comparisons alongside obtaining basins of attraction to compare them in the complex plane according to their convergence speed and chaotic behavior.
url http://dx.doi.org/10.1155/2013/837243
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AT stanfordshateyi aniterativesolverinthepresenceandabsenceofmultiplicityfornonlinearequations
AT gulcanozkum aniterativesolverinthepresenceandabsenceofmultiplicityfornonlinearequations
AT fazlollahsoleymani iterativesolverinthepresenceandabsenceofmultiplicityfornonlinearequations
AT stanfordshateyi iterativesolverinthepresenceandabsenceofmultiplicityfornonlinearequations
AT gulcanozkum iterativesolverinthepresenceandabsenceofmultiplicityfornonlinearequations
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