Theory and Modern Applications
Table 2 Second error analysis
\(\tau =\frac{1}{N}\), \(h=\frac{\pi }{M}(h=\frac{1}{M})\) | α | DFFDS method (53) | DFFDS method (54) | ||
|---|---|---|---|---|---|
maxerror | CPU time | maxerror | CPU time | ||
N = 100, M = 10 | 0.1 | 0.0037 | 0.058788 | 9.3583 × 10−4 | 0.053881 |
0.5 | 0.0039 | 0.058378 | 9.4699 × 10−4 | 0.053244 | |
0.9 | 0.0023 | 0.060307 | 7.6247 × 10−4 | 0.053522 | |
N = 225, M = 15 | 0.1 | 0.0016 | 0.209456 | 4.1057 × 10−4 | 0.188579 |
0.5 | 0.0019 | 0.211921 | 4.2000 × 10−4 | 0.193100 | |
0.9 | 0.0011 | 0.210560 | 3.4152 × 10−4 | 0.197266 | |
N = 400; M = 20 | 0.1 | 9.0086 × 10−4 | 0.842888 | 2.3168 × 10−4 | 0.782940 |
0.5 | 0.0011 | 0.833370 | 2.3836 × 10−4 | 0.783129 | |
0.9 | 6.5204 × 10−4 | 0.828719 | 1.9566 × 10−4 | 0.792377 | |
N = 625, M = 25 | 0.1 | 5.7434 × 10−4 | 2.649214 | 1.4782 × 10−4 | 2.573540 |
0.5 | 7.0500 × 10−4 | 2.483463 | 1.5264 × 10−4 | 2.563704 | |
0.9 | 4.3467 × 10−4 | 2.456029 | 1.2630 × 10−4 | 2.574958 | |
N = 900, M = 30 | 0.1 | 3.9925 × 10−4 | 7.453583 | 1.0280 × 10−4 | 7.316265 |
0.5 | 4.9746 × 10−4 | 6.869959 | 1.0641 × 10−4 | 7.299569 | |
0.9 | 3.1281 × 10−4 | 6.832467 | 8.8656 × 10−5 | 7.294004 | |
N = 1600; M = 40 | 0.1 | 2.2437 × 10−4 | 41.880124 | 5.7796 × 10−5 | 41.476774 |
0.5 | 2.8486 × 10−4 | 41.768273 | 6.0134 × 10−5 | 41.488002 | |
0.9 | 1.8595 × 10−4 | 41.786979 | 5.0550 × 10−5 | 41.670310 | |