An Efficient Family of Optimal Eighth-Order Iterative Methods for Solving Nonlinear Equations and Its Dynamics
The prime objective of this paper is to design a new family of optimal eighth-order iterative methods by accelerating the order of convergence of the existing seventh-order method without using more evaluations for finding simple root of nonlinear equations. Numerical comparisons have been carried o...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/569719 |
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| _version_ | 1832560475026489344 |
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| author | Anuradha Singh J. P. Jaiswal |
| author_facet | Anuradha Singh J. P. Jaiswal |
| author_sort | Anuradha Singh |
| collection | DOAJ |
| description | The prime objective of this paper is to design a new family of optimal eighth-order iterative methods by accelerating the order of convergence of the existing seventh-order method without using more evaluations for finding simple root of nonlinear equations. Numerical comparisons have been carried out to demonstrate the efficiency and performance of the proposed method. Finally, we have compared new method with some existing eighth-order methods by basins of attraction and observed that the proposed scheme is more efficient. |
| format | Article |
| id | doaj-art-532d979d5f4d4752a76a02ac415a3e75 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-532d979d5f4d4752a76a02ac415a3e752025-02-03T01:27:26ZengWileyJournal of Mathematics2314-46292314-47852014-01-01201410.1155/2014/569719569719An Efficient Family of Optimal Eighth-Order Iterative Methods for Solving Nonlinear Equations and Its DynamicsAnuradha Singh0J. P. Jaiswal1Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal, Madhya Pradesh 462051, IndiaDepartment of Mathematics, Maulana Azad National Institute of Technology, Bhopal, Madhya Pradesh 462051, IndiaThe prime objective of this paper is to design a new family of optimal eighth-order iterative methods by accelerating the order of convergence of the existing seventh-order method without using more evaluations for finding simple root of nonlinear equations. Numerical comparisons have been carried out to demonstrate the efficiency and performance of the proposed method. Finally, we have compared new method with some existing eighth-order methods by basins of attraction and observed that the proposed scheme is more efficient.http://dx.doi.org/10.1155/2014/569719 |
| spellingShingle | Anuradha Singh J. P. Jaiswal An Efficient Family of Optimal Eighth-Order Iterative Methods for Solving Nonlinear Equations and Its Dynamics Journal of Mathematics |
| title | An Efficient Family of Optimal Eighth-Order Iterative Methods for Solving Nonlinear Equations and Its Dynamics |
| title_full | An Efficient Family of Optimal Eighth-Order Iterative Methods for Solving Nonlinear Equations and Its Dynamics |
| title_fullStr | An Efficient Family of Optimal Eighth-Order Iterative Methods for Solving Nonlinear Equations and Its Dynamics |
| title_full_unstemmed | An Efficient Family of Optimal Eighth-Order Iterative Methods for Solving Nonlinear Equations and Its Dynamics |
| title_short | An Efficient Family of Optimal Eighth-Order Iterative Methods for Solving Nonlinear Equations and Its Dynamics |
| title_sort | efficient family of optimal eighth order iterative methods for solving nonlinear equations and its dynamics |
| url | http://dx.doi.org/10.1155/2014/569719 |
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