On a 4-Point Sixteenth-Order King Family of Iterative Methods for Solving Nonlinear Equations

Table 1

Test functions and their roots.

𝑓1(𝑥)=exp(𝑥)sin(𝑥)+ln(1+𝑥^2)	𝑥^∗=0
𝑓2(𝑥)=𝑥^15+𝑥^4+4𝑥^2−15	𝑥^∗=1.148538…
𝑓3(𝑥)=(𝑥−2)(𝑥^10+𝑥+1)exp(−𝑥−1)	𝑥^∗=2
𝑓4(𝑥)=(𝑥+1)exp(sin(𝑥))−𝑥^2exp(cos(𝑥))−1	𝑥^∗=0
𝑓5(𝑥)=sin^2(𝑥)−𝑥^2+1	𝑥^∗=1.40449165…
𝑓6(𝑥)=exp(−𝑥)−cos(𝑥)	𝑥^∗=0
𝑓7(𝑥)=ln(𝑥^2+𝑥+2)−𝑥+1	𝑥^∗=4.15259074…