Theory and Modern Applications
Table 4 Absolute errors for Example 2
From: Numerical solution of linear integral equations system using the Bernstein collocation method
| Presented method | ANN method | TQR | |||
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r = 1 | 2.66 × 10−5 | 4.92 × 10−5 | 1.16 × 10−2 | 9.28 × 10−4 | 8.32 × 10−3 | 8.07 × 10−3 |
r = 2 | 5.85 × 10−5 | 1.37 × 10−5 | 4.30 × 10−3 | 1.48 × 10−3 | 2.14 × 10−2 | 4.81 × 10−3 |
r = 3 | 8.55 × 10−5 | 2.04 × 10−5 | 2.04 × 10−3 | 4.43 × 10−3 | 3.01 × 10−2 | 3.71 × 10−2 |
r = 4 | 6.14 × 10−5 | 4.11 × 10−5 | 1.73 × 10−3 | 5.91 × 10−3 | 3.91 × 10−2 | 3.16 × 10−2 |
r = 5 | 3.89 × 10−5 | 9.44 × 10−5 | 8.01 × 10−4 | 7.94 × 10−3 | 1.12 × 10−1 | 4.24 × 10−1 |
r = 6 | 2.12 × 10−5 | 5.17 × 10−5 | 6.23 × 10−4 | 1.94 × 10−2 | 3.62 × 10−1 | 2.80 × 10−1 |
r = 7 | 1.11 × 10−5 | 2.71 × 10−5 | 5.37 × 10−4 | 4.13 × 10−2 | 8.54 × 10−2 | 1.78 × 10−1 |
r = 8 | 5.70 × 10−6 | 1.38 × 10−5 | 4.95 × 10−4 | 6.89 × 10−2 | 6.37 × 10−2 | 7.07 × 10−2 |
r = 9 | 2.90 × 10−6 | 7.01 × 10−6 | 4.75 × 10−4 | 9.40 × 10−2 | 8.64 × 10−2 | 9.04 × 10−3 |