Basins of attraction for Zhou–Chen–Song fourth order family of methods for multiple roots

A sixth-order family of three-point modified Newton-like multiple-root finders and the dynamics behind their extraneous fixed points

“…The dynamics underlying basins of attraction was initiated by Stewart [41] and followed by works of Amat et al [2][3][4][5] , Scott et al [38] , Chun et al [10] , Chun-Neta [11] , Chicharro et al [8] , Cordero et al [15] , Neta et al [28,33] , Argyros-Magreñan [7] , Magreñan [27] , Magreñan et al [26] , Andreu et al [6] and Chun et al [12] . The only papers comparing basins of attraction for methods to obtain multiple roots are due to Neta et al [29] , Neta-Chun [30,34] , Chun-Neta [13,14] and Geum-Kim-Neta [19] .…”

“…Other types of combinations have empirically shown poor convergence in the existing studies by [13,19,29,34] . A special attention will be paid to some selected cases 1A , 2A , 2B, 2C, 3A , 4A as well as all 5X and 5Y in order to pursue further properties of extraneous fixed points and relevant dynamics associated with their basins of attraction.…”

Comparing the basins of attraction for Kanwar–Bhatia–Kansal family to the best fourth order method

“…The third one choosing a quadratic polynomial for Q will not be considered here, since Chun and Neta [26] have shown that such a choice will give inferior results.…”

“…These methods were shown to perform better than other fourth order methods for multiple roots [42]. We also use ZCS1 and ZCS5 below, which were the best options suggested in [26].…”

“…The only papers comparing basins of attraction for methods to obtain multiple roots are due to Neta et al [41], Neta and Chun [18], [42], and Chun and Neta [26].…”