Open Access
2012 Another Simple Way of Deriving Several Iterative Functions to Solve Nonlinear Equations
Ramandeep Behl, V. Kanwar, Kapil K. Sharma
J. Appl. Math. 2012(SI06): 1-22 (2012). DOI: 10.1155/2012/294086


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.


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Ramandeep Behl. V. Kanwar. Kapil K. Sharma. "Another Simple Way of Deriving Several Iterative Functions to Solve Nonlinear Equations." J. Appl. Math. 2012 (SI06) 1 - 22, 2012.


Published: 2012
First available in Project Euclid: 3 January 2013

zbMATH: 1268.65064
MathSciNet: MR2997273
Digital Object Identifier: 10.1155/2012/294086

Rights: Copyright © 2012 Hindawi

Vol.2012 • No. SI06 • 2012
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