Table 2: Results of application of the proposed method for cases in which Newton or secant method fails to converge.

FunctionRootComparison of number of iterations required
Starting pointSecant methodNewton methodTwo-point Newton method

1.887207676120680111Oscillates7
0.523Oscillates6
1.0000000000000003.0FailsFails5
= arctan 0.00000000000003.0DivergesDiverges6
−3.0DivergesDiverges6
−1.1673039782614202.0OscillatesOscillates12
3.014Oscillates15
4.000000000000003.010Oscillates7
5.08Oscillates6
0.000000000000001.0OscillatesDiverges101
−1.0OscillatesDiverges101
1.6796306104284503.0DivergesDiverges8
0.101025848315685−1.0DivergesDiverges11