Theory and Modern Applications
Table 13 The absolute errors obtained by our method with \(N=4,10\) and \(\alpha =1\) along with the CPU time for Example 5
τ | \(\mathfrak{V}_{1}(\tau )\) | \(\mathfrak{V}_{2}(\tau )\) | \(\mathfrak{W}(\tau )\) | |||
|---|---|---|---|---|---|---|
N = 4 | N = 10 | N = 4 | N = 10 | N = 4 | N = 10 | |
0.1 | 8.155 × 10−5 | 3.247 × 10−14 | 1.067 × 10−4 | 5.942 × 10−14 | 4.695 × 10−5 | 1.659 × 10−14 |
0.2 | 5.210 × 10−5 | 6.518 × 10−14 | 5.954 × 10−5 | 1.171 × 10−13 | 1.849 × 10−5 | 3.106 × 10−14 |
0.3 | 1.353 × 10−4 | 1.663 × 10−13 | 1.695 × 10−4 | 2.877 × 10−13 | 6.724 × 10−5 | 6.810 × 10−14 |
0.4 | 9.583 × 10−5 | 1.746 × 10−13 | 1.272 × 10−4 | 2.946 × 10−13 | 5.656 × 10−5 | 6.411 × 10−14 |
0.5 | 2.195 × 10−5 | 1.625 × 10−14 | 1.779 × 10−5 | 1.930 × 10−14 | 1.211 × 10−6 | 1.975 × 10−15 |
0.6 | 1.248 × 10−4 | 1.593 × 10−13 | 1.508 × 10−4 | 2.764 × 10−13 | 5.491 × 10−5 | 6.597 × 10−14 |
0.7 | 1.311 × 10−4 | 1.792 × 10−13 | 1.663 × 10−4 | 3.030 × 10−13 | 6.734 × 10−5 | 6.653 × 10−14 |
0.8 | 2.411 × 10−5 | 8.725 × 10−14 | 3.714 × 10−5 | 1.433 × 10−13 | 1.984 × 10−5 | 2.837 × 10−14 |
0.9 | 1.017 × 10−4 | 4.781 × 10−14 | 1.229 × 10−4 | 7.761 × 10−14 | 4.597 × 10−5 | 1.473 × 10−14 |
1.0 | 6.838 × 10−8 | 6.470 × 10−18 | 6.756 × 10−8 | 4.836 × 10−17 | 0.0 | 2 × 10−20 |
CPU Time | 0.641 s | 0.765 s | – | – | – | – |