Abstract
We present a modification of Kurchatov's iterative method in order to solve a nonlinear equation with multiple roots, that is, for approximating solutions with multiplicity greater than one. One of its principal advantages is that you do not have to know a priori the multiplicity of the root, since it does not appear in the iterative expression. In order to examine the behaviour of the proposed method, we perform a dynamical analysis. Furthermore, we carry out some numerical experiments in order to confirm the theoretical results and compare the proposed method with other known methods for dealing with multiple roots.
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