Table 1 The absolute values of the error (53) of the composite trapezoidal rule for \(N=1, 10, 100, 1000\) and \(\omega =1.1, 10.1, 100.1, 1000.1\)
From: Optimal quadrature formulas for oscillatory integrals in the Sobolev space
ω = 1.1 | ω = 10.1 | ω = 100.1 | ω = 1000.1 | |
|---|---|---|---|---|
\(|I-A_{\mathrm{tr}}|\) | \(|I-A_{\mathrm{tr}}|\) | \(|I-A_{\mathrm{tr}}|\) | \(|I-A_{\mathrm{tr}}|\) | |
N = 1 | 3.874936(−1) | 3.063506(−1) | 2.951759(−1) | 2.940213(−1) |
N = 10 | 5.701761(−3) | 1.641521(−1) | 1.529774(−1) | 1.518228(−1) |
N = 100 | 5.639861(−5) | 4.407336(−4) | 1.529774(−1) | 1.504333(−1) |
N = 1000 | 5.639251(−7) | 4.376634(−6) | 4.278453(−5) | 1.504194(−1) |