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Zbl 1222.65048
Soleymani, Fazlollah
Revisit of Jarratt method for solving nonlinear equations. (English)
[J] Numer. Algorithms 57, No. 3, 377-388 (2011). ISSN 1017-1398; ISSN 1572-9265/e

The author proposes two sixth-order methods in a three-step cycle for solving single variable nonlinear equations where no evaluation of the second or higher derivatives is used. The first and second steps of the three-step cycle make use of the Jarratt method. In the third step, a fraction based on Padé approximant and Taylor expansion for estimating the first derivative of the function are used. The proposed algorithms require two evaluations of the function and two evaluations of the first derivatives. The convergence of the proposed iterative methods is established. Some numerical test results show that the accuracy and convergence radius of the proposed methods are comparable to other iterative methods of different orders.
[Hang Lau (Montréal)]

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

Keywords: nonlinear equation; Newton's method; Jarratt method; Padé approximant; error equation; simple root; derivative approximation; convergence radius; algorithms; numerical results

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