Journal of Applied Mathematics

Research Article

A Class of Three-Step Derivative-Free Root Solvers with Optimal Convergence Order

Table 2

Test functions and their roots.
Nonlinear functionsRoots
𝑓 1 ( 𝑥 ) = s i n ( 𝑥 ) − 𝑥 / 1 0 0 0
𝑓 2 ( 𝑥 ) = 1 / 3 𝑥 4 − 𝑥 2 − 1 / 3 𝑥 + 1 1
𝑓 3 ( 𝑥 ) = 𝑒 s i n ( 𝑥 ) − 1 − 𝑥 / 5 0
𝑓 4 ( 𝑥 ) = 𝑥 + s i n ( 𝑥 2 / 𝜋 ) 0
𝑓 5 √ ( 𝑥 ) = 𝑥 4 𝜋 + 8 s i n ( 𝑥 2 + 𝑥 + 2 ) 3 𝑥 4 − √ + 1 8 6 + 1 7 −2
𝑓 6 ( 𝑥 ) = a r c s i n ( 𝑥 2 𝑥 − 1 ) − 2 + 1 0.594810968398369
𝑓 7 ( 𝑥 ) = c o s ( 𝑥 ) − 𝑥 0.739085133215160
𝑓 8 ( 𝑥 ) = 𝑒 𝑥 + c o s 𝑥 −1.7461395304080124