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

Table 1

Test functions.

𝑓(𝑥)	𝛼	𝑚
𝑓1(𝑥)=((𝑥−1)^3−1)^6	2.0000000000000000000000000000	6
𝑓2(𝑥)=(ln(𝑥^2+𝑥+2)−𝑥+1)^4	4.1525907367571582749969890048	4
𝑓3(𝑥)=(ln^2(𝑥−2)𝑒^𝑥−3−1sin𝜋𝑥3)	3.0000000000000000000000000000	4
𝑓4(𝑥)=(𝑥^2−𝑒^𝑥−3𝑥+2)^5	0.2575302854398607604553673049	5
𝑓5(𝑥)=(cos𝑥−𝑥)^3	0.73908513321516064165531208767	3
𝑓6√1(𝑥)=(𝑥−𝑥−3)^3	9.6335955628326951924063127092	3
𝑓7(𝑥)=(𝑥^3−10)^8	2.1544346900318837217592935665	8