Theory and Modern Applications
Table 3 Absolute error for Example 3
From: Numerical solution of certain Cauchy singular integral equations using a collocation scheme
Node | Exact solution | Absolute error | Absolute error |
|---|---|---|---|
n = 8 and m = 10 | n = 10 and m = 10 | ||
−1.0 | 0.540302 | 5.63786 × 10−09 | 1.3509 × 10−11 |
−0.9 | 0.62161 | 5.08218 × 10−10 | 6.73017 × 10−13 |
−0.8 | 0.696707 | 4.88729 × 10−10 | 9.73333 × 10−13 |
−0.7 | 0.764842 | 2.94039 × 10−10 | 5.64326 × 10−13 |
−0.6 | 0.825336 | 1.09171 × 10−10 | 1.02507 × 10−12 |
−0.5 | 0.877583 | 3.27639 × 10−10 | 1.17395 × 10−12 |
−0.4 | 0.921061 | 6.6095 × 10−10 | 3.34288 × 10−13 |
−0.3 | 0.955336 | 6.70017 × 10−10 | 3.69038 × 10−13 |
−0.2 | 0.980067 | 2.78499 × 10−10 | 8.53762 × 10−14 |
−0.1 | 0.995004 | 1.83289 × 10−10 | 1.17184 × 10−12 |
0.0 | 1.0 | 2.9988 × 10−10 | 1.51223 × 10−12 |
0.1 | 0.995004 | 6.01889 × 10−11 | 5.87641 × 10−13 |
0.2 | 0.980067 | 6.12546 × 10−10 | 5.58442 × 10−13 |
0.3 | 0.955336 | 8.65893 × 10−10 | 4.71290 × 10−13 |
0.4 | 0.921061 | 5.43585 × 10−10 | 8.68305 × 10−13 |
0.5 | 0.877583 | 9.17413 × 10−11 | 1.70097 × 10−12 |
0.6 | 0.825336 | 3.52923 × 10−10 | 6.77236 × 10−13 |
0.7 | 0.764842 | 1.88950 × 10−10 | 5.97855 × 10−13 |
0.8 | 0.696707 | 8.80399 × 10−10 | 6.23279 × 10−13 |
0.9 | 0.621610 | 4.35435 × 10−10 | 1.58096 × 10−12 |
1.0 | 0.540302 | 1.58424 × 10−09 | 3.40161 × 10−12 |