A New Second-Order Iteration Method for Solving Nonlinear Equations | Zendy

Shin Min Kang | Zendy; Arif Rafiq | Zendy; Young Chel Kwun | Zendy

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A New Second-Order Iteration Method for Solving Nonlinear Equations

Author(s) -

Shin Min Kang,

Arif Rafiq,

Young Chel Kwun

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/487062

Subject(s) - mathematics , nonlinear system , convergence (economics) , newton's method , computation , simple (philosophy) , order (exchange) , operator (biology) , iterative method , fixed point iteration , fixed point , mathematical optimization , mathematical analysis , algorithm , philosophy , biochemistry , physics , chemistry , epistemology , quantum mechanics , finance , repressor , transcription factor , economics , gene , economic growth

We establish a new second-order iteration method for solving nonlinear equations. The efficiency index of the method is 1.4142which is the same as the Newton-Raphson method. By using some examples, the efficiency of the method is also discussed. It is worth to note that (i) our method is performing very well in comparison to the fixed point method and the method discussed in Babolian and Biazar (2002) and (ii) our method is so simple to apply in comparison to the method discussed in Babolian and Biazar (2002) and involves only first-order derivative but showing second-order convergence and this is not the case in Babolian and Biazar (2002), where the method requiresthe computations of higher-order derivatives of the nonlinear operator involved in the functional equation

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