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Revisit of Jarratt method for solving nonlinear equations. (English) Zbl 1222.65048
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.
65H05Single nonlinear equations (numerical methods)
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