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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Main Authors: Ramandeep Behl, V. Kanwar, Kapil K. Sharma
Format: Article
Language:English
Published: Wiley 2012-01-01
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
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institution Kabale University
issn 1110-757X
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language English
publishDate 2012-01-01
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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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