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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)