Optimal High-Order Methods for Solving Nonlinear Equations

Table 2

Comparison of modified-Gauss schemes for Orbit I.

	|(𝑥1−𝑥0)|	|𝐹(𝑥1)|	|(𝑥2−𝑥1)|	|𝐹(𝑥2)|	|(𝑥3−𝑥2)|	|𝐹(𝑥3)|	ACOC
FP	0.6450𝑒−2	—	0.8288𝑒−4	—	0.1055𝑒−5	—	1.002
K8	0.6368𝑒−2	0.2059𝑒−21	0.2033𝑒−21	0.6553𝑒−158	0.647𝑒−158	0.2164𝑒−1113	7.001
S8	0.6368𝑒−2	0.1377𝑒−23	0.1359𝑒−23	0.5565𝑒−197	0.5495𝑒−197	0.3967𝑒−1584	8.001
M8	0.6368𝑒−2	0.1382𝑒−23	0.1365𝑒−23	0.5791𝑒−197	0.5718𝑒−197	0.5488𝑒−1584	8.000
T16	0.6368𝑒−2	0.2662𝑒−63	0.2628𝑒−63	0.1642𝑒−1045	NaN	NaN	—
S16	0.6368𝑒−2	0.7454𝑒−48	0.7361𝑒−48	0.6647𝑒−783	0.6563𝑒−783	0.0	16.000
M16	0.6368𝑒−2	0.6998𝑒−47	0.6910𝑒−47	0.2286𝑒−766	0.2258𝑒−766	0.0	16.000