Theory and Modern Applications
Table 2 Numerical results for Example 1 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 | −0.0999 | 0.09 | 7.02 × 10−7 | 1.27 × 10−5 |
0.2 | −0.1984 | 0.16 | 2.10 × 10−6 | 2.07 × 10−5 |
0.3 | −0.2919 | 0.21 | 3.15 × 10−6 | 1.58 × 10−5 |
0.4 | −0.3744 | 0.24 | 3.71 × 10−6 | 1.28 × 10−5 |
0.5 | −0.4375 | 0.25 | 3.62 × 10−6 | 1.14 × 10−5 |
0.6 | −0.4704 | 0.24 | 3.30 × 10−6 | 1.11 × 10−5 |
0.7 | −0.4599 | 0.21 | 3.06 × 10−6 | 1.14 × 10−5 |
0.8 | −0.3904 | 0.16 | 2.22 × 10−6 | 1.01 × 10−5 |
0.9 | −0.2409 | 0.09 | 1.24 × 10−6 | 8.14 × 10−6 |
1 | 0 | 0 | 0 | 0 |