On a numerical technique for finding multiple zeros and its dynamic | Zendy

Fazlollah Soleymani | Zendy; D.K.R. Babajee | Zendy; Taher Lotfi | Zendy

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On a numerical technique for finding multiple zeros and its dynamic

Author(s) -

Fazlollah Soleymani,

D.K.R. Babajee,

Taher Lotfi

Publication year - 2013

Publication title -

journal of the egyptian mathematical society

Language(s) - English

Resource type - Journals

eISSN - 2090-9128

pISSN - 1110-256X

DOI - 10.1016/j.joems.2013.03.011

Subject(s) - multiplicity (mathematics) , mathematics , convergence (economics) , nonlinear system , fractal , mathematical optimization , mathematical analysis , physics , quantum mechanics , economics , economic growth

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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