Theory and Modern Applications
Table 3 Example 3: Maximum absolute errors \(\pmb{e_{m,\infty}}\) with \(\pmb{m=5 }\) , \(\pmb{\alpha=0.5 }\) , \(\pmb{\beta =0.5}\) and \(\pmb{L=3}\)
Ï„ | TQF | \(O(\tau^{2})\) | FDM | \(O(\tau^{2-\alpha})\) |
|---|---|---|---|---|
\(e_{5,\infty}(u)=e_{5,\infty}(v)\) | \(e_{5,\infty}(u)=e_{5,\infty }(v)\) | |||
0.015625 | 1.21322402 × 10−4 |  | 1.23475331 × 10−3 |  |
0.0078125 | 3.17697252 × 10−5 | 1.95 | 4.67009965 × 10−4 | 1.46 |
0.00390625 | 8.15383818 × 10−6 | 1.96 | 1.71676167 × 10−4 | 1.45 |
0.001953125 | 2.07020075 × 10−6 | 1.97 | 6.21304589 × 10−5 | 1.48 |