Commenced in January 2007
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Edition: International
Paper Count: 87758
An Optimal and Efficient Family of Fourth-Order Methods for Nonlinear Equations
Authors: Parshanth Maroju, Ramandeep Behl, Sandile S. Motsa
Abstract:
In this study, we proposed a simple and interesting family of fourth-order multi-point methods without memory for obtaining simple roots. This family requires only three functional evaluations (viz. two of functions f(xn), f(yn) and third one of its first-order derivative f'(xn)) per iteration. Moreover, the accuracy and validity of new schemes is tested by a number of numerical examples are also proposed to illustrate their accuracy by comparing them with the new existing optimal fourth-order methods available in the literature. It is found that they are very useful in high precision computations. Further, the dynamic study of these methods also supports the theoretical aspect.Keywords: basins of attraction, nonlinear equations, simple roots, Newton's method
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