On the new family of optimal eighth order methods developed by Lotfi et al.

Abstract

On the new family of optimal eighth order methods developed by Lotfi et al.Chun, Changbum Springer C. Chun, B. Neta, "On the new family of optimal eighth order methods developed by

Comparative study of eighth-order methods for finding simple roots of nonlinear equations

“…The idea of using basins of attraction appeared first in Stewart [3] and followed by the works of Amat et al [4][5][6] and [7], Scott et al [8], Chun et al [9], Chicharro et al [10], Cordero et al [11], Neta et al [12,13], Chun et al [14][15][16], Argyros and Magreñan [17], and Magreñan [18]. In later works ( [15,16,[19][20][21]), we have introduced a more quantitative comparison, by listing the average number of iterations per point, the CPU time, and the number of points requiring 40 iterations. We have also discussed how to choose the parameters appearing in the method and/or the weight function (see, e.g., [22]).…”

“…where t n is given by (15) and the weight function p(t) should satisfy the following condition to guarantee eighth order:…”

“…The next four methods were analyzed and compared to WL8 in [15] and found that they cannot compete with WL8. Therefore, we will not show those results here.…”

“…where r n is given by (14), t n is given by (15), and v n is given by (16). The weight functions H, K, G satisfy…”

Comparison of several families of optimal eighth order methods

“…In [11] we have compared several members of the family LSSS to the methods cited there and to the method by Wang and Liu [12] denoted WL which showed good results in our previous work (see, for example, Chun and Neta [11,13]. The method WL is as follows:…”