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...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2013/837243 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850163070884642816 |
|---|---|
| author | Fazlollah Soleymani Stanford Shateyi Gülcan Özkum |
| author_facet | Fazlollah Soleymani Stanford Shateyi Gülcan Özkum |
| author_sort | Fazlollah Soleymani |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-ef6d2c2193214a01ac2b9e9fd1534e9e |
| institution | OA Journals |
| issn | 1537-744X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-ef6d2c2193214a01ac2b9e9fd1534e9e2025-08-20T02:22:24ZengWileyThe 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 |
| spellingShingle | Fazlollah Soleymani Stanford Shateyi Gülcan Özkum An Iterative Solver in the Presence and Absence of Multiplicity for Nonlinear Equations The Scientific World Journal |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2013/837243 |
| work_keys_str_mv | AT fazlollahsoleymani aniterativesolverinthepresenceandabsenceofmultiplicityfornonlinearequations AT stanfordshateyi aniterativesolverinthepresenceandabsenceofmultiplicityfornonlinearequations AT gulcanozkum aniterativesolverinthepresenceandabsenceofmultiplicityfornonlinearequations AT fazlollahsoleymani iterativesolverinthepresenceandabsenceofmultiplicityfornonlinearequations AT stanfordshateyi iterativesolverinthepresenceandabsenceofmultiplicityfornonlinearequations AT gulcanozkum iterativesolverinthepresenceandabsenceofmultiplicityfornonlinearequations |