Another Simple Way of Deriving Several Iterative Functions to Solve Nonlinear Equations

Table 1

Test problems.

𝑓(𝑥)	[𝑎,𝑏]	Root (𝑟)
𝑓1𝑥(𝑥)=sin𝑥−2	[1.5,2]	1.895494222640991
𝑓2(𝑥)=cos𝑥−𝑥	[0,2]	0.739085137844086
𝑓3(𝑥)=𝑥^3−10	[2,4]	2.154434680938721
𝑓4(𝑥)=10𝑥𝑒^−𝑥2−1	[1,2]	1.679630637168884
𝑓5(𝑥)=(𝑥−1)^3−1	[1.5,3.5]	2.000000000000000
𝑓6(𝑥)=tan^−1𝑥−𝑥+1	[1.5,3]	2.132267713546753
𝑓7(𝑥)=𝑥^4−𝑥^3+11𝑥−7=0	[0,1]	0.645023941993713
𝑓8(𝑥)=𝑥^5+17𝑥=0	[−0.5,1]	0
𝑓9(𝑥)=𝑥^3−cos𝑥+2=0	[−2,−1]	−1.172577977180481
𝑓10(𝑥)=𝑒^𝑥2+7𝑥−30−1=0	[2.9,3.5]	3