Theory and Modern Applications
Table 1 First error analysis
\(\tau =\frac{1}{N}\), \(h=\frac{\pi }{M}(h=\frac{1}{M})\) | α | IFDS method (53) | IFDS method (54) | ||
|---|---|---|---|---|---|
maxerror | CPU time | maxerror | CPU time | ||
N = 100, M = 10 | 0.1 | 0.0028 | 0.098552 | 6.2342 × 10−4 | 0.053605 |
0.5 | 0.0031 | 0.084086 | 6.4051 × 10−4 | 0.052642 | |
0.9 | 0.0015 | 0.085630 | 4.6868 × 10−4 | 0.054644 | |
N = 225, M = 15 | 0.1 | 0.0012 | 0.250553 | 2.7629 × 10−4 | 0.192028 |
0.5 | 0.0014 | 0.207235 | 2.8823 × 10−4 | 0.189281 | |
0.9 | 7.6017 × 10−4 | 0.209145 | 2.1545 × 10−4 | 0.190512 | |
N = 400; M = 20 | 0.1 | 6.9287 × 10−4 | 0.865346 | 1.5651 × 10−4 | 0.781243 |
0.5 | 8.0721 × 10−4 | 0.803135 | 1.6457 × 10−4 | 0.786518 | |
0.9 | 4.6721 × 10−4 | 0.801428 | 1.2512 × 10−4 | 0.796842 | |
N = 625, M = 25 | 0.1 | 4.1218 × 10−4 | 2.523352 | 1.0002 × 10−4 | 2.602625 |
0.5 | 5.2127 × 10−4 | 2.663734 | 1.0570 × 10−4 | 2.620778 | |
0.9 | 3.1690 × 10−4 | 2.688309 | 8.1457 × 10−5 | 2.620732 | |
N = 900, M = 30 | 0.1 | 3.0755 × 10−4 | 7.401635 | 6.9628 × 10−5 | 7.366031 |
0.5 | 3.6546 × 10−4 | 7.372820 | 7.3836 × 10−5 | 7.383805 | |
0.9 | 2.3088 × 10−4 | 7.361036 | 5.7533 × 10−5 | 7.390021 | |
N = 1600; M = 40 | 0.1 | 1.1793 × 10−4 | 41.706692 | 3.9181 × 10−5 | 41.866478 |
0.5 | 2.0757 × 10−4 | 41.839637 | 4.1731 × 10−5 | 41.602334 | |
0.9 | 1.3883 × 10−4 | 41.987633 | 2.6572 × 10−5 | 41.437862 | |