Theory and Modern Applications
Table 4 Comparison between FSG(C-N) and FSkG(C-N) iterative methods at \(\tau =1/10\) for Example 1
\(h^{-1}\) | Method | Execution time (sec.) | Ite. | Ave error | Max error | Total operations |
|---|---|---|---|---|---|---|
α = 0.65 | ||||||
10 | FSG(C-N) | 2.93282 | 20 | 4.71168 × 10−2 | 9.69517 × 10−2 | 403,380 |
FSkG(C-N) | 1.10761 | 12 | 4.88586 × 10−2 | 1.00569 × 10−1 | 132,468 | |
15 | FSG(C-N) | 12.5737 | 35 | 4.41042 × 10−2 | 9.71679 × 10−2 | 1,708,140 |
FSkG(C-N) | 4.30563 | 21 | 4.48098 × 10−2 | 9.87645 × 10−2 | 539,334 | |
20 | FSG(C-N) | 35.2718 | 54 | 4.26392 × 10−2 | 9.72095 × 10−2 | 4,854,006 |
FSkG(C-N) | 11.6689 | 32 | 4.30456 × 10−2 | 9.81329 × 10−2 | 1,487,028 | |
25 | FSG(C-N) | 78.9365 | 75 | 4.17918 × 10−2 | 9.75259 × 10−2 | 10,756,800 |
FSkG(C-N) | 25.1786 | 44 | 4.20595 × 10−2 | 9.81334 × 10−2 | 3,232,394 | |
α = 0.75 | ||||||
10 | FSG(C-N) | 2.26201 | 16 | 3.82775 × 10−2 | 7.67695 × 10−2 | 322,704 |
FSkG(C-N) | 0.90480 | 10 | 3.98710 × 10−2 | 8.01500 × 10−2 | 112,050 | |
15 | FSG(C-N) | 9.42246 | 27 | 3.58042 × 10−2 | 7.83929 × 10−2 | 1,317,708 |
FSkG(C-N) | 3.33842 | 17 | 3.64650 × 10−2 | 7.98128 × 10−2 | 441,228 | |
20 | FSG(C-N) | 26.3018 | 41 | 3.46193 × 10−2 | 7.86265 × 10−2 | 3,685,449 |
FSkG(C-N) | 8.81406 | 25 | 3.49882 × 10−2 | 7.94765 × 10−2 | 1,171,545 | |
25 | FSG(C-N) | 57.9856 | 58 | 3.39374 × 10−2 | 7.85311 × 10−2 | 8,318,592 |
FSkG(C-N) | 18.6265 | 34 | 3.41800 × 10−2 | 7.91150 × 10−2 | 2,514,029 | |
α = 0.85 | ||||||
10 | FSG(C-N) | 1.87201 | 13 | 2.39638 × 10−2 | 5.27844 × 10−2 | 262,197 |
FSkG(C-N) | 0.79561 | 9 | 2.53145 × 10−2 | 5.55785 × 10−2 | 101,841 | |
15 | FSG(C-N) | 7.36325 | 21 | 2.24018 × 10−2 | 5.21491 × 10−2 | 1,024,884 |
FSkG(C-N) | 2.71442 | 13 | 2.29590 × 10−2 | 5.34259 × 10−2 | 343,122 | |
20 | FSG(C-N) | 20.1397 | 32 | 2.17059 × 10−2 | 5.27656 × 10−2 | 2,876,448 |
FSkG(C-N) | 6.89524 | 19 | 2.20033 × 10−2 | 5.34685 × 10−2 | 901,131 | |
25 | FSG(C-N) | 44.0391 | 44 | 2.13271 × 10−2 | 5.25357 × 10−2 | 6,310,656 |
FSkG(C-N) | 14.6017 | 26 | 2.15153 × 10−2 | 5.29944 × 10−2 | 1,939,337 | |