Theory and Modern Applications
Table 5 Comparison between FSG(C-N) and FSkG(C-N) iterative methods \(\tau =1/15\) for Example 2
\(h^{-1}\) | Method | Execution time (sec.) | Ite. | Ave error | Max error | Total operations |
|---|---|---|---|---|---|---|
α = 0.60 | ||||||
12 | FSG(C-N) | 12.3553 | 26 | 1.13977 × 10−2 | 3.04174 × 10−2 | 1,145,144 |
FSkG(C-N) | 4.27443 | 16 | 1.12180 × 10−2 | 3.11192 × 10−2 | 377,104 | |
16 | FSG(C-N) | 34.7570 | 40 | 1.12653 × 10−2 | 3.04467 × 10−2 | 3,276,000 |
FSkG(C-N) | 11.0605 | 24 | 1.11831 × 10−2 | 3.08253 × 10−2 | 1,027,936 | |
20 | FSG(C-N) | 78.3905 | 57 | 1.11666 × 10−2 | 3.08420 × 10−2 | 7,490,028 |
FSkG(C-N) | 25.7246 | 33 | 1.11369 × 10−2 | 3.09775 × 10−2 | 2,239,692 | |
24 | FSG(C-N) | 150.182 | 76 | 1.10778 × 10−2 | 3.09794 × 10−2 | 14,634,256 |
FSkG(C-N) | 48.0327 | 44 | 1.10844 × 10−2 | 3.11293 × 10−2 | 4,340,336 | |
α = 0.70 | ||||||
12 | FSG(C-N) | 8.82966 | 19 | 8.23924 × 10−3 | 2.59719 × 10−2 | 836,836 |
FSkG(C-N) | 3.26042 | 12 | 8.21954 × 10−3 | 2.65085 × 10−2 | 288,288 | |
16 | FSG(C-N) | 24.1490 | 29 | 8.06517 × 10−3 | 2.63727 × 10−2 | 2,375,100 |
FSkG(C-N) | 8.40845 | 18 | 8.06394 × 10−3 | 2.66746 × 10−2 | 781,144 | |
20 | FSG(C-N) | 53.4459 | 41 | 7.96695 × 10−3 | 2.65627 × 10−2 | 5,387,564 |
FSkG(C-N) | 17.5189 | 24 | 7.98367 × 10−3 | 2.67728 × 10−2 | 1,646,736 | |
24 | FSG(C-N) | 104.567 | 54 | 7.89936 × 10−3 | 2.66550 × 10−2 | 10,398,024 |
FSkG(C-N) | 32.7290 | 32 | 7.93508 × 10−3 | 2.68291 × 10−2 | 3,182,816 | |
α = 0.80 | ||||||
12 | FSG(C-N) | 6.61444 | 14 | 1.15550 × 10−2 | 2.71116 × 10−2 | 616,616 |
FSkG(C-N) | 2.69882 | 10 | 1.15107 × 10−2 | 2.76285 × 10−2 | 243,880 | |
16 | FSG(C-N) | 17.3941 | 21 | 1.11922 × 10−2 | 2.74914 × 10−2 | 1,719,900 |
FSkG(C-N) | 6.55204 | 13 | 1.11648 × 10−2 | 2.76485 × 10−2 | 575,484 | |
20 | FSG(C-N) | 37.9550 | 28 | 1.09646 × 10−2 | 2.75706 × 10−2 | 3,679,312 |
FSkG(C-N) | 13.2445 | 18 | 1.09317 × 10−2 | 2.76839 × 10−2 | 1,251,432 | |
24 | FSG(C-N) | 72.2909 | 37 | 1.08101 × 10−2 | 2.76601 × 10−2 | 7,124,572 |
FSkG(C-N) | 23.9930 | 22 | 1.07676 × 10−2 | 2.76683 × 10−2 | 2,218,216 | |