Table 5 Errors obtained and CPU time (seconds) for Example 7.5 using various values for \(\alpha, \beta \) at different N
α | β | Errors | N = 1 | N = 3 | N = 5 | N = 7 | N = 9 | N = 11 |
|---|---|---|---|---|---|---|---|---|
0 | 0 | \(\|E_{N}\|_{\infty}\) | 1.56×10−2 | 5.83×10−5 | 6.18×10−8 | 5.19×10−11 | 2.98×10−14 | 6.66×10−16 |
|  |  | \(\|E_{N}\|_{2}\) | 9.71×10−3 | 1.21×10−5 | 3.83×10−8 | 3.26×10−11 | 1.83×10−14 | 6.20×10−16 |
| Â | Â | CPU time | 0.123 | 0.311 | 0.402 | 0.423 | 0.425 | 0.512 |
1 | 0 | \(\|E_{N}\|_{\infty}\) | 3.19×10−2 | 1.21×10−4 | 2.07×10−7 | 7.92×10−11 | 1.24×10−13 | 6.66×10−16 |
|  |  | \(\|E_{N}\|_{2}\) | 8.53×10−3 | 2.55×10−5 | 3.73×10−8 | 3.20×10−11 | 1.81×10−14 | 3.26×10−16 |
| Â | Â | CPU time | 0.124 | 0.313 | 0.404 | 0.426 | 0.428 | 0.514 |
0 | 1 | \(\|E_{N}\|_{\infty}\) | 3.42×10−2 | 1.35×10−4 | 2.39×10−7 | 2.37×10−10 | 1.50×10−13 | 6.66×10−16 |
|  |  | \(\|E_{N}\|_{2}\) | 2.50×10−2 | 9.73×10−5 | 1.69×10−7 | 1.65×10−10 | 1.03×10−13 | 5.50×10−16 |
| Â | Â | CPU time | 0.123 | 0.312 | 0.402 | 0.424 | 0.427 | 0.512 |
1/2 | 1/2 | \(\|E_{N}\|_{\infty}\) | 1.79×10−2 | 4.98×10−5 | 7.91×10−8 | 6.43×10−11 | 3.84×10−14 | 8.88×10−16 |
|  |  | \(\|E_{N}\|_{2}\) | 8.66×10−3 | 2.87×10−5 | 4.34×10−8 | 3.80×10−11 | 2.18×10−14 | 4.01×10−16 |
| Â | Â | CPU time | 0.120 | 0.309 | 0.398 | 0.410 | 0.419 | 0.497 |
1 | 2 | \(\|E_{N}\|_{\infty}\) | 3.81×10−2 | 1.94×10−4 | 4.12×10−7 | 5.02×10−10 | 3.77×10−13 | 3.61×10−16 |
|  |  | \(\|E_{N}\|_{2}\) | 2.66×10−3 | 1.53×10−4 | 3.52×10−7 | 4.27×10−10 | 3.20×10−13 | 1.23×10−16 |
| Â | Â | CPU time | 0.129 | 0.381 | 0.422 | 0.443 | 0.445 | 0.552 |