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

Table 1

The test functions considered in this study.

Test functions	Zeros	Initial guesses
𝑓1(𝑥)=3𝑥+sin(𝑥)−𝑒^𝑥	𝛼1≈0.360421702960324	𝑥0=0.5
𝑓2(𝑥)=sin(𝑥)−0.5	𝛼2≈0.523598775598299	𝑥0=0.3
𝑓3(𝑥)=𝑥𝑒^−𝑥−0.1	𝛼3≈0.111832559158963	𝑥0=0.2
𝑓4(𝑥)=𝑥^3−10	𝛼4≈2.15443490031884	𝑥0=1.7
𝑓5(𝑥)=10𝑥𝑒^−𝑥2−1	𝛼5≈1.679630610428450	𝑥0=1.4
𝑓6(𝑥)=cos(𝑥)−𝑥	𝛼6≈0.739085133215161	𝑥0=0.3