On a numerical technique for finding multiple zeros and its dynamic

By Fazlollah Soleymani, Diyashvir Kreetee Rajiv Babajee, Taher Lotfi. 2013

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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.

Subfields: Mathematical Physics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/5c3fe49d942563bcd8c7e2f05d9dff7892a2baa7