Abstract
Abstract An optimal method is developed for approximating the multiple zeros of a nonlinear function, when the multiplicity is known. Analysis of convergence for the proposed technique is studied to reveal the fourth-order convergence. We further investigate the dynamics of such multiple zero finders by using basins of attraction and their corresponding fractals in the complex plane. A fourth-order method will also be presented, when the multiplicity m is not known. Numerical comparisons will be made to support the underlying theory of this paper.
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