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

Table 2

Performance of the methods using 12 NFE.

𝑓(𝑥)	𝑥0	|𝑒𝑘|=|𝑥𝑘−𝛼|
		MNM	OM	HM	SSM (𝛽=3/2)	CNM	SBM (𝐶=1/2)
𝑓1	1.75	1.20 (−34)	2.76 (−22)	5.48 (−34)	4.01 (−41)	1.08 (−42)	1.25 (−22)
	3	1.55 (−16)	2.75 (−15)	4.93 (−18)	2.36 (−20)	6.78 (−21)	2.37 (−15)
𝑓2	4	4.53 (−129)	4.46 (−137)	1.46 (−145)	1.17 (−144)	1.11 (−141)	1.75 (−137)
	5	6.88 (−86)	2.45 (−84)	7.75 (−91)	3.78 (−90)	7.10 (−88)	1.19 (−84)
𝑓3	2.5	5.41 (−67)	2.47 (−76)	8.33 (−57)	5.60 (−63)	4.90 (−58)	1.34 (−74)
	3.25	7.83 (−99)	2.32 (−118)	1.39 (−106)	2.61 (−110)	2.60 (−107)	2.35 (−115)
𝑓4	−2	1.55 (−37)	1.30 (−42)	1.45 (−40)	1.52 (−39)	1.47 (−40)	2.52 (−40)
	1.5	1.06 (−57)	2.44 (−50)	5.15 (−50)	2.43 (−40)	4.66 (−38)	1.33 (−49)
𝑓5	0.3	3.59 (−59)	2.13 (−44)	5.12 (−64)	5.12 (−64)	7.17 (−53)	1.16 (−47)
	1.7	3.25 (−65)	5.35 (−41)	2.25 (−44)	2.25 (−44)	1.84 (−42)	1.66 (−41)
𝑓6	9	5.13 (−108)	2.51 (−137)	1.50 (−135)	1.50 (−135)	1.15 (−193)	9.43 (−146)
	10	1.11 (−61)	3.59 (−158)	4.68 (−157)	4.68 (−157)	9.07 (−214)	7.54 (−167)
𝑓7	2	2.59 (−72)	1.68 (−78)	6.75 (−99)	3.89 (−89)	3.29 (−92)	1.44 (−78)
	3	2.79 (−33)	3.19 (−34)	2.97 (−47)	9.07 (−41)	8.73 (−43)	2.92 (−34)

Here 𝑎(−𝑏)=𝑎×10^−𝑏.