Theory and Modern Applications
Table 5 Example 4: Maximum absolute errors \(\pmb{e_{m,\infty}}\) with \(\pmb{\tau=1/64}\) , \(\pmb{\alpha=\beta=1}\) and \(\pmb{L=3}\)
m | TQF | FDM | ||
|---|---|---|---|---|
u(x,t) | v(x,t) | u(x,t) | v(x,t) | |
5 | 2.56389687 × 10−3 | 2.56389687 × 10−3 | 2.12780543 × 10−3 | 2.12780543 × 10−3 |
7 | 1.19107232 × 10−3 | 1.19107232 × 10−3 | 1.06246855 × 10−4 | 1.06246855 × 10−4 |
9 | 6.89082786 × 10−4 | 6.89082786 × 10−4 | 1.71691547 × 10−6 | 1.71691547 × 10−6 |
11 | 5.71482080 × 10−4 | 5.71482080 × 10−4 | 1.98386814 × 10−8 | 1.98386814 × 10−8 |