Theory and Modern Applications
Table 4 Numerical results for Example 2 when \(\pmb{N=40}\)
x | Exact sol. in u | Exact sol. in v | Absolute error in u | Absolute error in v |
|---|---|---|---|---|
0 | 0 | 0 | 0 | 0 |
0.1 | −0.009 | 0.09 | 7.43 × 10−6 | 8.46 × 10−5 |
0.2 | −0.032 | 0.16 | 8.57 × 10−6 | 1.37 × 10−4 |
0.3 | −0.063 | 0.21 | 8.29 × 10−6 | 1.23 × 10−4 |
0.4 | −0.096 | 0.24 | 8.64 × 10−6 | 1.15 × 10−4 |
0.5 | −0.125 | 0.25 | 9.17 × 10−6 | 1.09 × 10−4 |
0.6 | −0.144 | 0.24 | 9.58 × 10−6 | 1.03 × 10−4 |
0.7 | −0.147 | 0.21 | 9.58 × 10−6 | 9.36 × 10−5 |
0.8 | −0.128 | 0.16 | 8.70 × 10−6 | 7.32 × 10−5 |
0.9 | −0.081 | 0.09 | 5.90 × 10−6 | 4.53 × 10−5 |
1 | 0 | 0 | 0 | 0 |