Theory and Modern Applications
Table 3 The MAEs of Example 3
γ | Our method at (N,M,K) \(\alpha _{1}=\beta _{1}=\alpha _{2}=\beta _{2}=\frac {1}{2}\), \(\alpha _{3}=\beta _{3}=0\) | Explicit numerical approximation scheme [43] | ||
|---|---|---|---|---|
(4,4,6) | (4,4,12) | \((\frac{1}{4},\frac {1}{4},\frac{1}{900})\) | \((\frac{1}{8},\frac{1}{8},\frac{1}{4900})\) | |
0.7 | 2.147706 × 10−3 | 1.351622 × 10−4 | 1.823187 × 10−3 | 4.963875 × 10−4 |
0.8 | 1.246139 × 10−3 | 8.543486 × 10−5 | 1.825094 × 10−3 | 4.959106 × 10−4 |
0.9 | 5.288470 × 10−4 | 6.502807 × 10−5 | 1.826525 × 10−3 | 4.968643 × 10−4 |
γ | Our method at (N,M,K) \(\alpha _{1}=\beta _{1}=\alpha _{2}=\beta _{2}=\frac {1}{2}\), \(\alpha _{3}=\beta _{3}=0\) | Implicit numerical approximation scheme [43] | ||
|---|---|---|---|---|
(6,6,6) | (6,6,24) | \((\frac{1}{8},\frac {1}{8},\frac{1}{64})\) | \((\frac{1}{32},\frac{1}{32},\frac {1}{1024})\) | |
0.7 | 1.351622 × 10−4 | 7.517080 × 10−6 | 1.350407 × 10−3 | 1.456738 × 10−4 |
0.8 | 6.878345 × 10−5 | 3.349460 × 10−6 | 1.451373 × 10−3 | 2.348423 × 10−4 |
0.9 | 2.558291 × 10−5 | 1.090555 × 10−6 | 1.657724 × 10−3 | 3.523827 × 10−4 |