Theory and Modern Applications
Table 1 The MAEs of Example 1
(N,M) | Our method with \(\alpha _{1}=\beta _{1}=\frac{1}{2}\), \(\alpha _{2}=\beta _{2}=0\) and several choices of γ | ||
|---|---|---|---|
0.5 | 0.6 | 0.7 | |
(8,8) | 4.40262 × 10−5 | 3.40111 × 10−5 | 2.36798 × 10−5 |
(8,16) | 9.00183 × 10−7 | 6.07094 × 10−7 | 3.68766 × 10−7 |
(8,32) | 2.3328 × 10−8 | 1.92534 × 10−8 | 1.35477 × 10−8 |
\(\tau=h^{2}\) | Implicit numerical approximation scheme [41] | ||
|---|---|---|---|
0.5 | 0.6 | 0.7 | |
\(\frac{1}{64}\) | 2.9530 × 10−3 | 3.2886 × 10−3 | 3.6359 × 10−3 |
\(\frac{1}{256}\) | 7.6212 × 10−4 | 8.4259 × 10−4 | 9.2593 × 10−4 |
\(\frac{1}{1024}\) | 2.0744 × 10−4 | 2.2061 × 10−4 | 2.2671 × 10−4 |