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Table 1 Errors and orders in time for \(J=1024, t=1\)

From: Conservative Fourier spectral scheme for the coupled Schrödinger–Boussinesq equations

   τ 0.05 0.025 0.0125 0.00625
u \(l_{h}^{2}\) error 8.750 × 10−5 2.188 × 10−5 5.470 × 10−6 1.367 × 10−6
order * 1.99 2.00 2.00
\(l_{h}^{\infty}\) error 4.179 × 10−5 1.060 × 10−5 2.692 × 10−6 6.765 × 10−7
order * 1.97 1.97 2.00
v \(l_{h}^{2}\) error 1.150 × 10−4 2.880 × 10−5 7.211 × 10−6 1.803 × 10−6
order * 1.99 1.99 1.99
\(l_{h}^{\infty}\) error 7.487 × 10−5 1.92 × 10−5 4.862 × 10−6 1.223 × 10−6
order * 1.96 1.98 1.99