General Family of Third Order Methods for Multiple Roots of Nonlinear Equations and Basin Attractors for Various Methods
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Date
2014
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Hindawi Publishing Corporation Advances in Numerical Analysis Volume 2014, Article ID 963878, 8 pages
Abstract
A general scheme of third order convergence is described for finding multiple roots of nonlinear equations. The proposed scheme
requires one evaluation of 𝑓, 𝑓
, and 𝑓 each per iteration and contains several known one-point third order methods for finding
multiple roots, as particular cases. Numerical examples are included to confirm the theoretical results and demonstrate convergence
behavior of the proposed methods. In the end, we provide the basins of attraction for some methods to observe their dynamics in
the complex plane.