Theory and Modern Applications
Table 2 The MAEs of Example 2
(N,M) | Our method with \(\alpha _{1}=\beta _{1}=\frac{1}{2}\), \(\alpha _{2}=\beta _{2}=0\) and several choices of γ | ||
|---|---|---|---|
0.4 | 0.5 | 0.6 | |
(4,4) | 7.27394 × 10−3 | 6.35126 × 10−3 | 5.08519 × 10−3 |
(4,12) | 1.81744 × 10−4 | 1.29398 × 10−4 | 8.43394 × 10−4 |
(4,36) | 6.87762 × 10−6 | 5.42605 × 10−6 | 3.79045 × 10−6 |
\(\tau=h^{2}\) | Fourier method and an extrapolation technique [42] | ||
|---|---|---|---|
0.4 | 0.5 | 0.6 | |
\(\frac{1}{4}\) | 7.0342 × 10−3 | 1.0336 × 10−2 | 1.3420 × 10−2 |
\(\frac{1}{64}\) | 8.2629 × 10−4 | 1.0360 × 10−3 | 1.1898 × 10−3 |
\(\frac{1}{1024}\) | 8.2731 × 10−5 | 7.5748 × 10−5 | 1.3471 × 10−4 |