Some Iterative Methods Free from Derivatives and Their Basins of Attraction for Nonlinear Equations

Figure 4

Fractal behavior for the rational function associated to the Steffensen’s method with 𝛽=0.01 (a), Jain’s method (b), (3) with 𝛽=0.01 (c) and (3) with 𝛽=0.0001 (d) for 𝑓∶𝑧→𝑧⁴+1. Shading according to the number of iterations.

(a)

(b)

(c)

(d)