General Family of Third Order Methods for Multiple Roots of Nonlinear Equations and Basin Attractors for Various Methods

Figure 1

Basins of attraction for (𝑧)=(𝑧²−1)²,  𝑧∈𝐷, for various methods of the family.

(a) The modified Newton method

(b) The Osada method

(c) Halley’s method

(d) The Chun-Neta method

(e) The Sharma-Sharma method (𝛽=3/2)

(f) SBM (𝐶=1/2)