Theory and Modern Applications
Table 9 The comparison of absolute errors with the method in [25] for \(N=5\) and 8 in Example 3
τ | N = 5 | N = 8 | ||||
|---|---|---|---|---|---|---|
\(\mathfrak{V}_{1}(\tau )\) | \(\mathfrak{V}_{2}(\tau )\) | \(\mathfrak{W}(\tau )\) | \(\mathfrak{V}_{1}(\tau )\) | \(\mathfrak{V}_{2}(\tau )\) | \(\mathfrak{W}(\tau )\) | |
The results obtained in [25] | ||||||
0.0 | 5.0873 × 10−3 | 1.1759 × 10−4 | 3.7671 × 10−2 | 6.4701 × 10−4 | 9.2045 × 10−8 | 2.7317 × 10−3 |
0.2 | 1.3401 × 10−3 | 9.6759 × 10−6 | 6.1908 × 10−3 | 2.4746 × 10−5 | 7.0205 × 10−10 | 5.9560 × 10−4 |
0.4 | 4.8751 × 10−4 | 1.7241 × 10−6 | 1.1315 × 10−2 | 5.0303 × 10−5 | 1.1698 × 10−9 | 1.2007 × 10−4 |
0.6 | 4.3069 × 10−4 | 4.3754 × 10−7 | 1.0657 × 10−2 | 3.4906 × 10−5 | 9.3245 × 10−10 | 7.3763 × 10−5 |
0.8 | 1.2658 × 10−3 | 7.6358 × 10−6 | 4.7850 × 10−3 | 3.8725 × 10−5 | 1.6391 × 10−9 | 5.4601 × 10−4 |
1.0 | 4.8997 × 10−3 | 1.1139 × 10−4 | 3.4480 × 10−2 | 6.4545 × 10−4 | 8.9541 × 10−8 | 2.5760 × 10−3 |
The results obtained by our method | ||||||
0.0 | 0.0 | 2 × 10−20 | 3.6908 × 10−9 | 0.0 | 8.0 × 10−20 | 5.6978 × 10−16 |
0.2 | 2.3436 × 10−5 | 2.1666 × 10−5 | 7.8041 × 10−6 | 5.8730 × 10−9 | 4.3139 × 10−9 | 1.8615 × 10−9 |
0.4 | 1.6825 × 10−5 | 1.5141 × 10−5 | 5.4356 × 10−6 | 8.0689 × 10−9 | 5.9364 × 10−9 | 2.5491 × 10−9 |
0.6 | 7.0832 × 10−6 | 7.1373 × 10−6 | 2.5745 × 10−6 | 7.8782 × 10−9 | 5.7997 × 10−9 | 2.4855 × 10−9 |
0.8 | 2.1970 × 10−5 | 2.0483 × 10−5 | 7.3610 × 10−6 | 5.0522 × 10−9 | 3.7254 × 10−9 | 1.5878 × 10−9 |
1.0 | 4.7942 × 10−8 | 3.0254 × 10−8 | 2.0 × 10−20 | 6.9046 × 10−15 | 4.0177 × 10−15 | 6.0 × 10−21 |