On a numerical technique for finding multiple zeros and its dynamic

Journal of the Egyptian Mathematical Society

F. Soleymani¹  Taher Lotfi²  D.K.R. Babajee³ 

[1] Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran;Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran;Scientific & Academic Research Council, African Network for Policy Research & Advocacy for Sustainability, Mauritius;

关键词: Basins of attraction;    Fractal;    Multiplicity;    Numerical solution;    Dynamic;   

DOI  :  10.1016/j.joems.2013.03.011

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown