Theory and Modern Applications
Table 11 A comparison between the absolute errors obtained by our method with those obtained in [48] with \(N=5\) for Example 4
τ | Our method | Method in [48] | ||
|---|---|---|---|---|
\(\mathfrak{V}(\tau )\) | \(\mathfrak{W}(\tau )\) | \(\mathfrak{V}(\tau )\) | \(\mathfrak{W}(\tau )\) | |
0.0 | 0.0 | 4.7460 × 10−20 | 5.1454 × 10−27 | 2.7547 × 10−4 |
0.1 | 2.2357 × 10−20 | 5.5117 × 10−20 | 5.9358 × 10−5 | 3.3361 × 10−5 |
0.2 | 2.4210 × 10−20 | 4.4821 × 10−20 | 4.9622 × 10−5 | 4.2236 × 10−5 |
0.3 | 1.9896 × 10−20 | 2.8470 × 10−20 | 2.3649 × 10−5 | 9.7096 × 10−5 |
0.4 | 1.7317 × 10−20 | 1.4329 × 10−20 | 7.1658 × 10−6 | 5.7043 × 10−5 |
0.5 | 1.9448 × 10−20 | 6.4627 × 10−21 | 6.1834 × 10−6 | 1.3750 × 10−5 |
0.6 | 2.5851 × 10−20 | 4.7187 × 10−21 | 1.4421 × 10−5 | 3.8228 × 10−5 |
0.7 | 3.4182 × 10−20 | 5.6070 × 10−21 | 2.0724 × 10−5 | 3.7231 × 10−6 |
0.8 | 4.1702 × 10−20 | 4.5163 × 10−21 | 1.6485 × 10−5 | 5.7195 × 10−5 |
0.9 | 4.6790 × 10−20 | 1.2947 × 10−22 | 3.0606 × 10−6 | 2.9022 × 10−5 |
1.0 | 5.0449 × 10−20 | 2.1746 × 10−36 | 8.0434 × 10−7 | 1.0987 × 10−4 |