Table 3 The numerical results for \(\pmb{t=0.25}\)
From: Asymptotic expansions of the error for hyper-singular integrals with an interval variable
h | \(\boldsymbol{2^{3}}\) | \(\boldsymbol{2^{4}}\) | \(\boldsymbol{2^{5}}\) | \(\boldsymbol{2^{6}}\) | \(\boldsymbol{2^{7}}\) | \(\boldsymbol{2^{8}}\) |
|---|---|---|---|---|---|---|
Q(h) | 1.3382 | 1.8031 | 2.7290 | 4.5797 | 8.2808 | 15.6830 |
\(\overline{Q}^{(0)}(h)\) | 0.87321 | 0.87726 | 0.87827 | 0.87852 | 0.87859 | |
\(|\overline{Q}^{(0)}(h)-I|\) | 5.3987e − 3 | 1.3502e − 3 | 3.3757e − 4 | 8.4394e − 5 | 2.1099e − 5 | |
\(r_{n}^{(1)}\) | 21.9995 | 21.9999 | 22.0000 | 22.0000 | 22.0000 | |
\(\overline{Q}^{(1)}(h)\) | 0.878607 | 0.878608 | 0.878608 | 0.878608 | ||
\(|\overline{Q}^{(1)}(h)-I|\) | 6.5498e − 7 | 3.8287e − 8 | 2.3688e − 9 | 1.4785e − 10 | ||
\(r_{n}^{(2)}\) | 24.0965 | 24.0146 | 24.0020 | 23.9961 |