An Iterative Solver in the Presence and Absence of Multiplicity for Nonlinear Equations. (22nd December 2013)

• Record Type: Journal Article
• Authors: Soleymani, Fazlollah; Shateyi, Stanford; Özkum, Gülcan
• Other Names: Amat S. Academic Editor.; Inc M. Academic Editor.; Mukandavire Z. Academic Editor.; Ostrovska S. Academic Editor.; Qin X. Academic Editor.; Tersian S. A. Academic Editor.
• Is Part Of: TheScientificWorldjournal. Volume 2013(2013)
• Publication Date: 2013-12-22
• Subjects: Science -- Periodicals; Technology -- Periodicals; Medicine -- Periodicals; 505
• DOI: 10.1155/2013/837243
• Languages: English
• ISSNs: 2356-6140

Abstract

Abstract : We develop a high-order fixed point type method to approximate a multiple root. By using three functional evaluations per full cycle, a new class of fourth-order methods for this purpose is suggested and established. The methods from the class require the knowledge of the multiplicity. We also present a method in the absence of multiplicity for nonlinear equations. In order to attest the efficiency of the obtained methods, we employ numerical comparisons alongside obtaining basins of attraction to compare them in the complex plane according to their convergence speed and chaotic behavior.