Algorithms, Volume 14, Issue 4 (April 2021) – 27 articles
Cover Story (view full-size image): A new parametric family of three-step iterative procedures for approximating the solutions of nonlinear equations is presented. The analysis of convergence proves the sixth-order of all members of the class. Using complex dynamics, wide areas of the complex plane are found where the corresponding value of the parameter yields a stable iterative scheme. Moreover, some other regions are found whose respective iterative methods have chaotic or unstable behavior. Several test functions are analyzed to check the analytical and dynamical information. Some of the proposed methods are shown to be very efficient and can converge from initial estimations far from the searched solution. View this paper.
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