A Family of Fourteenth-Order Convergent Iterative Methods for Solving Nonlinear Equations

Table 1

Numerical examples.

Examples	Exact zero
𝑓1(𝑥)=(𝑥−1)^3−1,	𝑥^∗=2.0000000000000000000
𝑓2(𝑥)=√𝑥^2+2𝑥+5−2sin𝑥−𝑥^2+3	𝑥^∗=2.3319676558839640103
𝑓3(𝑥)=𝑥^3−10	𝑥^∗=2.1544346900318837217
𝑓4(𝑥)=𝑥^5+𝑥−10,000	𝑥^∗=6.3087771299726890947
𝑓5(𝑥)=√1𝑥−𝑥−3	𝑥^∗=9.6335955628326951924
𝑓6(𝑥)=𝑒^𝑥+𝑥−20	𝑥^∗=2.8424389537844470678
𝑓7(𝑥)=ln𝑥+√𝑥−5	𝑥^∗=8.3094326942315717953
𝑓8(𝑥)=𝑥^5+𝑥^4+4𝑥^2−15	𝑥^∗=1.3474280989683049815
𝑓9(𝑥)=𝑒^−𝑥2+𝑥+2−1	𝑥^∗=−1.000000000000000000
𝑓10(𝑥)=arcsin(𝑥^21−1)−2𝑥+1	𝑥^∗=0.5948109683983691775
𝑓11(𝑥)=10𝑥𝑒^−𝑥2−1	𝑥^∗=1.67963061042844994067
𝑓12(𝑥)=sin^2𝑥−𝑥^2+1	𝑥^∗=1.40449164821534122603
𝑓13(𝑥)1=sin𝑥−𝑥	𝑥^∗=−0.8975394612804871843
𝑓14(𝑥)=𝑥^3−3𝑥^2+𝑥−2	𝑥^∗=2.89328919630449778890
𝑓15(𝑥)=cos^2𝑥𝑥−5	𝑥^∗=2.32020427449572608989