Theory and Modern Applications
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 |