An optimal fourth order weighted-Newton method for computing multiple roots and basin attractors for various methods
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Date
2016
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Pelagia Research Library Advances in Applied Science Research, 2016, 7(4):47-54
Abstract
In this paper, we present an optimal fourth order method for finding multiple roots of a nonlinear equation f(x)=0.
In terms of computational cost, the method uses one evaluation of the function and two evaluations of its first
derivative per iteration. Therefore, the method has optimal order with efficiency index 1.587 which is better than
efficiency indices 1.414 of Newton method, 1.442 of Halley’s method and 1.414 of Neta-Johnson method. Numerical
examples are given to support that the method thus obtained is competitive with other similar robust methods. The
basins of attraction of the proposed method are presented and compared with other existing methods.