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Zbl 1189.65091
Dehghan, Mehdi; Hajarian, Masoud
Some derivative free quadratic and cubic convergence iterative formulas for solving nonlinear equations. (English)
[J] Comput. Appl. Math. 29, No. 1, 19-30 (2010). ISSN 0101-8205; ISSN 1807-0302/e

The authors propose four methods based on the central-difference and forward-difference approximations to the derivatives for solving nonlinear equations. Three of the four methods are proved to have cubic convergence and the fourth method has quadratic convergence. Two numerical examples are presented to compare the four methods with the Newton's method and Steffensen's method.
[Hang Lau (Montréal)]

MSC 2000:: *65H05 Single nonlinear equations (numerical methods)

Keywords: Newton's method; cubic convergence; quadratic convergence; nonlinear equations; iterative method; numerical examples; Steffensen's method

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