Abstract
In this paper, we have suggested and analyzed a new two-step type iterative methods for solving nonlinear equations of the type. We show that this new two-step method is cubic convergence method. It is proved that this method is better than the Newton method and all results in (Soheili et al., 2008). Several examples are given to illustrate the efficiency of this new method and its comparison with other methods. This method can se considered as a significant improvement of the Newton method and its variant forms.
Highlights
IntroductionAnalytical methods for solving such equations are difficult or almost non-existent
Iterative methods for finding the roots of nonlinear equations f (x) = 0 are common yet important problem in science and engineering
We show that this new two-step method is cubic convergence method
Summary
Analytical methods for solving such equations are difficult or almost non-existent It has been shown in (Noor, 2006b) that these quadrature formulas can be used to develop some iterative methods for solving nonlinear equations, we have suggested and analyzed new iterative method by using the Newton and the Halley (Noor & Inayat Noor, 2007) methods and some newly developed method by (Noor, 2006a; Noor & Inayat Noor, 2007; Noor & Ahmad, 2006a) as predictor method and use this new method as a corrector method. All test problems reveals a good accuracy and fast convergence of the new method
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