Another Simple Way of Deriving Several Iterative Functions to Solve Nonlinear Equations
We present another simple way of deriving several iterative methods for solving nonlinear equations numerically. The presented approach of deriving these methods is based on exponentially fitted osculating straight line. These methods are the modifications of Newton's method. Also, we obtain we...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/294086 |
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| author | Ramandeep Behl V. Kanwar Kapil K. Sharma |
| author_facet | Ramandeep Behl V. Kanwar Kapil K. Sharma |
| author_sort | Ramandeep Behl |
| collection | DOAJ |
| description | We present another simple way of deriving several iterative methods for solving nonlinear equations numerically. The presented approach of deriving these methods is based on exponentially fitted osculating straight line. These methods are the modifications of Newton's method. Also, we obtain well-known methods as special cases, for example, Halley's method, super-Halley method, Ostrowski's square-root method, Chebyshev's method, and so forth. Further, new classes of third-order multipoint iterative methods free from a second-order derivative are derived by semidiscrete modifications of cubically convergent iterative methods. Furthermore, a simple linear combination of two third-order multipoint iterative methods is used for designing new optimal methods of order four. |
| format | Article |
| id | doaj-art-8797c58b6a59401bbf9fd9bcc43972dc |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-8797c58b6a59401bbf9fd9bcc43972dc2025-08-20T03:37:43ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/294086294086Another Simple Way of Deriving Several Iterative Functions to Solve Nonlinear EquationsRamandeep Behl0V. Kanwar1Kapil K. Sharma2Department of Mathematics, Panjab University, Chandigarh 160 014, IndiaUniversity Institute of Engineering and Technology, Panjab University, Chandigarh 160 014, IndiaDepartment of Mathematics, Panjab University, Chandigarh 160 014, IndiaWe present another simple way of deriving several iterative methods for solving nonlinear equations numerically. The presented approach of deriving these methods is based on exponentially fitted osculating straight line. These methods are the modifications of Newton's method. Also, we obtain well-known methods as special cases, for example, Halley's method, super-Halley method, Ostrowski's square-root method, Chebyshev's method, and so forth. Further, new classes of third-order multipoint iterative methods free from a second-order derivative are derived by semidiscrete modifications of cubically convergent iterative methods. Furthermore, a simple linear combination of two third-order multipoint iterative methods is used for designing new optimal methods of order four.http://dx.doi.org/10.1155/2012/294086 |
| spellingShingle | Ramandeep Behl V. Kanwar Kapil K. Sharma Another Simple Way of Deriving Several Iterative Functions to Solve Nonlinear Equations Journal of Applied Mathematics |
| title | Another Simple Way of Deriving Several Iterative Functions to Solve Nonlinear Equations |
| title_full | Another Simple Way of Deriving Several Iterative Functions to Solve Nonlinear Equations |
| title_fullStr | Another Simple Way of Deriving Several Iterative Functions to Solve Nonlinear Equations |
| title_full_unstemmed | Another Simple Way of Deriving Several Iterative Functions to Solve Nonlinear Equations |
| title_short | Another Simple Way of Deriving Several Iterative Functions to Solve Nonlinear Equations |
| title_sort | another simple way of deriving several iterative functions to solve nonlinear equations |
| url | http://dx.doi.org/10.1155/2012/294086 |
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