Table 2: Numerical results from 𝑓 1 to 𝑓 1 0 and seventh-order schemes.
H F M S K M N M M 7
𝑓 1 , 𝑥 0 = 0 . 9 | 𝑥 𝑘 + 1 − 𝑥 𝑘 | 9 . 2 4 0 3 𝑒 − 0 5 0 7 . 8 9 9 5 𝑒 − 1 0 4 1 . 9 4 5 6 𝑒 − 0 2 3
| 𝑓 ( 𝑥 𝑘 + 1 ) | 0 0 1 . 8 1 0 1 𝑒 − 1 5 9
ACOC — 7.00236.6629
iter 6 ≥ 1 0 0 4 3
e-time 0.1126 0.14040.0927
𝑓 2 , 𝑥 0 = 1 . 2 | 𝑥 𝑘 + 1 − 𝑥 𝑘 | 1 . 1 6 0 2 𝑒 − 0 4 5 1 . 0 2 0 3 𝑒 − 0 3 6 6 . 3 7 4 7 𝑒 − 0 5 8 3 . 1 0 5 0 𝑒 − 0 2 9
| 𝑓 ( 𝑥 𝑘 + 1 ) | 0 00 1 . 0 4 9 5 𝑒 − 2 0 2
ACOC 6.7965 7.24036.7108 6.8723
iter 3 43 3
e-time 0.0604 0.14450.1100 0.1075
𝑓 3 , 𝑥 0 = 2 . 1 | 𝑥 𝑘 + 1 − 𝑥 𝑘 | 1 . 8 8 1 0 𝑒 − 0 4 0 9 . 8 6 1 2 𝑒 − 0 3 7 1 . 4 4 6 8 𝑒 − 0 5 2 5 . 6 4 9 5 𝑒 − 0 2 4
| 𝑓 ( 𝑥 𝑘 + 1 ) | 0 00 3 . 7 4 8 9 𝑒 − 1 6 7
ACOC 6.3228 6.24016.5225 7.0731
iter 3 43 3
e-time 0.0315 0.09690.0674 0.0468
𝑓 4 , 𝑥 0 = 2 . 2 | 𝑥 𝑘 + 1 − 𝑥 𝑘 | 5 . 1 0 6 4 𝑒 − 0 3 4 — 9 . 9 9 8 5 𝑒 − 0 4 2 3 . 4 7 0 9 𝑒 − 0 2 7
| 𝑓 ( 𝑥 𝑘 + 1 ) | 0— 0 5 . 1 7 8 1 𝑒 − 1 8 4
ACOC 6.8073— 6.91776.8325
iter 3n.c. 33
e-time 0.0532— 0.08420.0930
𝑓 5 , 𝑥 0 = 2 . 3 | 𝑥 𝑘 + 1 − 𝑥 𝑘 | 2 . 6 8 4 5 𝑒 − 0 5 3 3 . 2 1 0 7 𝑒 − 0 2 5 1 . 2 3 9 9 𝑒 − 0 6 2 1 . 2 6 3 8 𝑒 − 0 3 0
| 𝑓 ( 𝑥 𝑘 + 1 ) | 3 . 1 1 4 7 𝑒 − 2 0 7 9 . 9 1 4 6 𝑒 − 1 6 7 3 . 1 1 4 7 𝑒 − 2 0 7 6 . 8 4 6 3 𝑒 − 2 0 7
ACOC 6.9527 7.16516.9798 6.8181
iter 3 53 3
e-time 0.0406 0.08940.0961 0.0596
𝑓 6 , 𝑥 0 = 2 | 𝑥 𝑘 + 1 − 𝑥 𝑘 | 8 . 6 3 3 2 𝑒 − 1 2 4 1 . 0 5 4 7 𝑒 − 0 7 5 5 . 4 7 4 1 𝑒 − 0 2 3
| 𝑓 ( 𝑥 𝑘 + 1 ) | 0 0 9 . 2 4 9 1 𝑒 − 1 5 7
ACOC 6.99906.99485.9331
iter 4 ≥ 1 0 0 43
e-time 0.09110.14090.1226
𝑓 7 , 𝑥 0 = 0 . 5 | 𝑥 𝑘 + 1 − 𝑥 𝑘 | 8 . 9 8 7 9 𝑒 − 0 7 6 6 . 4 3 3 5 𝑒 − 0 4 5 1 . 6 6 0 7 𝑒 − 0 2 8 4 . 7 8 7 2 𝑒 − 0 3 4
| 𝑓 ( 𝑥 𝑘 + 1 ) | 3 . 8 9 3 4 𝑒 − 2 0 8 1 . 9 4 6 7 𝑒 − 2 0 8 1 . 1 7 0 7 𝑒 − 1 9 5 3 . 8 4 3 4 𝑒 − 2 0 8
ACOC 7.01156.87347.2394 6.8055
iter 433 3
e-time 0.07470.07570.1214 0.0732
𝑓 8 , 𝑥 0 = 1 . 5 | 𝑥 𝑘 + 1 − 𝑥 𝑘 | 2 . 1 4 2 4 𝑒 − 0 5 3 8 . 0 6 9 3 𝑒 − 0 6 3 1 . 1 2 4 9 𝑒 − 0 3 0
| 𝑓 ( 𝑥 𝑘 + 1 ) | 00 9 . 3 4 4 2 𝑒 − 2 0 7
ACOC 6.9528 6.97836.7788
iter 3 ≥ 1 0 0 33
e-time 0.07300.09670.1170
𝑓 9 , 𝑥 0 = 0 . 8 | 𝑥 𝑘 + 1 − 𝑥 𝑘 | 1 . 6 4 0 8 𝑒 − 0 2 7 1 . 3 5 2 8 𝑒 − 1 2 8 4 . 3 7 1 1 𝑒 − 0 3 9 6 . 1 0 7 3 𝑒 − 0 2 8
| 𝑓 ( 𝑥 𝑘 + 1 ) | 1 . 5 5 0 9 𝑒 − 1 9 0 2 . 4 3 3 4 𝑒 − 2 0 8 1 . 2 1 6 7 𝑒 − 2 0 8 1 . 6 5 8 2 𝑒 − 1 9 1
ACOC 7.32436.99997.1316 6.7613
iter 34 3 4
e-time 0.05520.1158 0.11120.1232
𝑓 1 0 , 𝑥 0 = 0 . 6 | 𝑥 𝑘 + 1 − 𝑥 𝑘 | 2 . 0 0 8 9 𝑒 − 0 3 5 — 1 . 1 0 4 6 𝑒 − 0 5 1 2 . 7 2 0 7 𝑒 − 0 1 9
| 𝑓 ( 𝑥 𝑘 + 1 ) | 0— 0 2 . 1 7 8 5 𝑒 − 1 6 7
ACOC 10.9352— 10.92178.7406
iter 3n.c. 33
e-time 0.0367— 0.09220.0749