Three New Optimal Fourth-Order Iterative Methods to Solve Nonlinear Equations

Table 1

List of functions for a single root.

𝑓1(𝑥)=𝑥^3+4𝑥^2−10,	𝑟=1.3652300134140968457608068290,
𝑓2(𝑥)=cos(𝑥)−𝑥,	𝑟=0.73908513321516064165531208767,
𝑓3(𝑥)=sin(𝑥)−(1/2)𝑥,	𝑟=1.8954942670339809471440357381,
𝑓4(𝑥)=sin^2(𝑥)−𝑥^2+1,	𝑟=1.4044916482153412260350868178,
𝑓5(𝑥)=𝑥𝑒^𝑥2−sin^2(𝑥)+3cos(𝑥)+5,	𝑟=1.2076478271309189270094167584,
𝑓6(𝑥)=𝑥^2−𝑒^𝑥−3𝑥+2,	𝑟=0.257530285439860760455367304944,
𝑓7(𝑥)=(𝑥−1)^3−2,	𝑟=2.2599210498948731647672106073,
𝑓8(𝑥)=(𝑥−1)^2−1,	𝑟=2,
𝑓9(𝑥)=10𝑥𝑒^−𝑥2−1,	𝑟=1.6796306104284499,
𝑓10(𝑥)=(𝑥+2)𝑒^𝑥−1,	𝑟=−0.4428544010023885831413280000,
𝑓11(𝑥)=𝑒^−𝑥+cos(𝑥).	𝑟=1.746139530408012417650703089.