Theory and Modern Applications
Table 3 Absolute errors for Example 1 by the proposed method at \(t=1\) when \(\alpha= 0.7\), \(N=100\), and \(\Delta t= 0.001\)
z/t→ | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 |
|---|---|---|---|---|---|---|---|---|---|
0.1 | 7.77 × 10−7 | 6.86 × 10−7 | 6.29 × 10−7 | 6.03 × 10−7 | 6.15 × 10−7 | 6.79 × 10−7 | 8.13 × 10−7 | 1.04 × 10−6 | 1.41 × 10−6 |
0.2 | 1.47 × 10−6 | 1.30 × 10−6 | 1.19 × 10−6 | 1.15 × 10−6 | 1.17 × 10−6 | 1.30 × 10−6 | 1.57 × 10−6 | 2.03 × 10−6 | 2.75 × 10−6 |
0.3 | 2.01 × 10−6 | 1.78 × 10−6 | 1.63 × 10−6 | 1.57 × 10−6 | 1.62 × 10−6 | 1.81 × 10−6 | 2.20 × 10−6 | 2.87 × 10−6 | 3.91 × 10−6 |
0.4 | 2.35 × 10−6 | 2.08 × 10−6 | 1.91 × 10−6 | 1.85 × 10−6 | 1.91 × 10−6 | 2.14 × 10−6 | 2.62 × 10−6 | 3.44 × 10−6 | 4.69 × 10−6 |
0.5 | 2.47 × 10−6 | 2.19 × 10−6 | 2.01 × 10−6 | 1.94 × 10−6 | 2.01 × 10−6 | 2.26 × 10−6 | 2.77 × 10−6 | 3.64 × 10−6 | 4.98 × 10−6 |
0.6 | 2.35 × 10−6 | 2.08 × 10−6 | 1.91 × 10−6 | 1.85 × 10−6 | 1.91 × 10−6 | 2.14 × 10−6 | 2.62 × 10−6 | 3.44 × 10−6 | 4.69 × 10−6 |
0.7 | 2.01 × 10−6 | 1.78 × 10−6 | 1.63 × 10−6 | 1.57 × 10−6 | 1.62 × 10−6 | 1.81 × 10−6 | 2.20 × 10−6 | 2.87 × 10−6 | 3.91 × 10−6 |
0.8 | 1.47 × 10−6 | 1.30 × 10−6 | 1.19 × 10−6 | 1.15 × 10−6 | 1.17 × 10−6 | 1.30 × 10−6 | 1.57 × 10−6 | 2.03 × 10−6 | 2.75 × 10−6 |
0.9 | 7.77 × 10−7 | 6.86 × 10−7 | 6.29 × 10−7 | 6.03 × 10−7 | 6.15 × 10−7 | 6.79 × 10−7 | 8.13 × 10−7 | 1.04 × 10−6 | 1.41 × 10−6 |