Theory and Modern Applications
Table 1 Absolute error for Example 1
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 | 0.0 | 8.57103 × 10−12 | 1.29419 × 10−11 | 1.71944 × 10−11 |
−0.9 | −0.171 | 5.28733 × 10−12 | 4.82814 × 10−12 | 3.02805 × 10−12 |
−0.8 | −0.288 | 2.76978 × 10−12 | 7.42573 × 10−13 | 2.76779 × 10−13 |
−0.7 | −0.357 | 9.33587 × 10−13 | 8.03413 × 10−13 | 4.52971 × 10−14 |
−0.6 | −0.384 | 3.06755 × 10−13 | 9.32199 × 10−13 | 6.80345 × 10−13 |
−0.5 | −0.375 | 1.03606 × 10−12 | 4.42868 × 10−13 | 6.23890 × 10−13 |
−0.4 | −0.336 | 1.33976 × 10−12 | 1.39888 × 10−13 | 1.88183 × 10−14 |
−0.3 | −0.273 | 1.30285 × 10−12 | 5.21860 × 10−13 | 6.22891 × 10−13 |
−0.2 | −0.192 | 1.01039 × 10−12 | 5.92443 × 10−13 | 8.7802 × 10−13 |
−0.1 | −0.099 | 5.47729 × 10−13 | 3.78711 × 10−13 | 6.14328 × 10−13 |
0.0 | 0.0 | 7.83203 × 10−17 | 3.64086 × 10−17 | 9.54481 × 10−17 |
0.1 | 0.099 | 5.47895 × 10−13 | 3.78794 × 10−13 | 6.14148 × 10−13 |
0.2 | 0.192 | 1.01058 × 10−12 | 5.92471 × 10−13 | 8.77770 × 10−13 |
0.3 | 0.273 | 1.30296 × 10−12 | 5.21916 × 10−13 | 6.22558 × 10−13 |
0.4 | 0.336 | 1.33993 × 10−12 | 1.39944 × 10−13 | 1.91513 × 10−14 |
0.5 | 0.375 | 1.03628 × 10−12 | 4.42868 × 10−13 | 6.24223 × 10−13 |
0.6 | 0.384 | 3.06977 × 10−13 | 9.32199 × 10−13 | 6.80678 × 10−13 |
0.7 | 0.357 | 9.33309 × 10−13 | 8.03468 × 10−13 | 4.56302 × 10−14 |
0.8 | 0.288 | 2.76945 × 10−12 | 7.42573 × 10−13 | 2.76501 × 10−13 |
0.9 | 0.171 | 5.28688 × 10−12 | 4.82803 × 10−12 | 3.02883 × 10−12 |
1.0 | 0.0 | 8.57059 × 10−12 | 1.29418 × 10−11 | 1.71959 × 10−11 |