Further Development of Jarratt Method for Solving Nonlinear Equations

Table 1

Test functions and their roots.

Functions	Roots
𝑓1(𝑥)=exp(𝑥)sin(𝑥)+ln(1+𝑥^2)	𝛼=0
𝑓2(𝑥)=(𝑥^2−1)^−1−1	𝛼=√2
𝑓3(𝑥)=(𝑥−2)(𝑥^10+𝑥+1)exp(−𝑥−1)	𝛼=2
𝑓4(𝑥)=(𝑥+1)exp(sin(𝑥))−𝑥^2exp(cos(𝑥))−1	𝛼=0
𝑓5(𝑥)=sin(𝑥)^2−𝑥^2+1	𝛼=1.40449165…
𝑓6(𝑥)=exp(−𝑥)−cos(𝑥),	𝛼=−0.666273126…
𝑓7(𝑥)=ln(𝑥^2+𝑥+2)−𝑥+1	𝛼=4.15259074…
𝑓8(𝑥)=𝑥^10−2𝑥^3−𝑥+1	𝛼=0.591448093…
𝑓9(𝑥)=cos(𝑥)^2−5^−1𝑥	𝛼=1.08598268…
𝑓10(𝑥)=sin(𝑥)−2^−1𝑥	𝛼=0