Theory and Modern Applications
Table 2 Absolute error for Example 2
From: Numerical solution of certain Cauchy singular integral equations using a collocation scheme
Node | Exact solution | Absolute error | Absolute error | Absolute error |
|---|---|---|---|---|
n = 3 and m = 16 | n = 5 and m = 16 | n = 7 and m = 16 | ||
−1.0 | −1.17520 | 1.91441 × 10−3 | 1.81254 × 10−5 | 8.91703 × 10−8 |
−0.9 | −1.02652 | 7.55784 × 10−4 | 4.56592 × 10−6 | 1.21329 × 10−8 |
−0.8 | −0.888106 | 3.26831 × 10−4 | 2.70516 × 10−6 | 1.01281 × 10−8 |
−0.7 | −0.758584 | 3.04940 × 10−4 | 3.37668 × 10−6 | 7.32927 × 10−9 |
−0.6 | −0.636654 | 4.56464 × 10−4 | 3.09250 × 10−6 | 2.74983 × 10−10 |
−0.5 | −0.521095 | 6.23736 × 10−4 | 1.48584 × 10−6 | 1.38631 × 10−9 |
−0.4 | −0.410752 | 7.12864 × 10−4 | 4.85742 × 10−7 | 4.69581 × 10−9 |
−0.3 | −0.30452 | 6.82151 × 10−4 | 1.69887 × 10−6 | 1.28989 × 10−8 |
−0.2 | −0.201336 | 5.31044 × 10−4 | 1.50059 × 10−6 | 1.59589 × 10−8 |
−0.1 | −0.100167 | 2.89494 × 10−4 | 6.72324 × 10−8 | 1.08082 × 10−8 |
0.0 | 0.0 | 7.61784 × 10−6 | 2.34882 × 10−6 | 5.43884 × 10−10 |
0.1 | 0.100167 | 2.54435 × 10−4 | 4.35718 × 10−6 | 7.79669 × 10−9 |
0.2 | 0.201336 | 4.36513 × 10−4 | 5.15723 × 10−6 | 7.95496 × 10−9 |
0.3 | 0.30452 | 4.88499 × 10−4 | 4.24896 × 10−6 | 1.03862 × 10−9 |
0.4 | 0.410752 | 3.80444 × 10−4 | 1.85014 × 10−6 | 1.32656 × 10−8 |
0.5 | 0.521095 | 1.12900 × 10−4 | 1.02282 × 10−6 | 1.89303 × 10−8 |
0.6 | 0.636654 | 2.72436 × 10−4 | 2.77923 × 10−6 | 1.16573 × 10−8 |
0.7 | 0.758584 | 6.81671 × 10−4 | 1.89035 × 10−6 | 3.30044 × 10−9 |
0.8 | 0.888106 | 9.57141 × 10−4 | 1.95203 × 10−6 | 7.44314 × 10−9 |
0.9 | 1.02652 | 8.65196 × 10−4 | 6.03881 × 10−6 | 1.32789 × 10−8 |
1.0 | 1.17520 | 8.32275 × 10−5 | 2.08619 × 10−6 | 1.23370 × 10−8 |