General Family of Third Order Methods for Multiple Roots of Nonlinear Equations and Basin Attractors for Various Methods. (31st March 2014)

• Record Type: Journal Article
• Authors: Sharma, Rajni; Bahl, Ashu
• Other Names: Huang Ting-Zhu Academic Editor.
• Is Part Of: Advances in numerical analysis. Volume 2014(2014)
• Publication Date: 2014-03-31
• Subjects: Numerical analysis -- Periodicals; Numerical analysis; Periodicals; Electronic journals; 518
• DOI: 10.1155/2014/963878
• Languages: English
• ISSNs: 1687-9562

Abstract

Abstract : A general scheme of third order convergence is described for finding multiple roots of nonlinear equations. The proposed scheme requires one evaluation off, f ′, andf ′′ each per iteration and contains several known one-point third order methods for finding multiple roots, as particular cases. Numerical examples are included to confirm the theoretical results and demonstrate convergence behavior of the proposed methods. In the end, we provide the basins of attraction for some methods to observe their dynamics in the complex plane.