Theory and Modern Applications
Table 8 Absolute errors for Example 2 at \(t=0.1\) with \(\Delta t=0.001\), \(\alpha= 0.5\), \(N=10\), and \(z\in[0,1]\)
z | Exact solution | Approximate solution | Error |
|---|---|---|---|
0.1 | 0.0005017 | 0.0005368 | 3.511 × 10−5 |
0.2 | 0.0009149 | 0.0009807 | 6.575 × 10−5 |
0.3 | 0.0011690 | 0.0012574 | 8.838 × 10−5 |
0.4 | 0.0012259 | 0.0013269 | 1.010 × 10−4 |
0.5 | 0.0010907 | 0.0011941 | 1.034 × 10−4 |
0.6 | 0.0008133 | 0.0009103 | 9.700 × 10−5 |
0.7 | 0.0004801 | 0.0005638 | 8.364 × 10−5 |
0.8 | 0.0001930 | 0.0002574 | 6.448 × 10−5 |
0.9 | 0.0000319 | 0.0000702 | 3.827 × 10−5 |