Open AccessOn a numerical technique for finding multiple zeros and its dynamic
Author(s) -
Fazlollah Soleymani,
Diyashvir Kreetee Rajiv 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