Theory and Modern Applications
Table 3 Spatial convergence rates for the proposed methods for Example 4.2 with fixed spatial resolution \(h=1/4000\)
\(J_{x}\) | σ = 100, ν = 0.1 | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
EAC3 | EAC4 | |||||||||
\(E_{\infty }(t)\) | \(\mathit{rate}_{t}\) | \(E_{R2}(t)\) | \(\mathit{rate}_{t}\) | cpu | \(E_{\infty }(t)\) | \(\mathit{rate}_{t}\) | \(E_{R2}(t)\) | \(\mathit{rate}_{t}\) | cpu | |
23 | 8.11 × 10−4 | – | 8.97 × 10−4 | – | 0.72 | 8.10 × 10−4 | – | 8.97 × 10−4 | – | 0.71 |
24 | 1.33 × 10−4 | 2.61 | 1.32 × 10−4 | 2.77 | 1.34 | 1.33 × 10−4 | 2.61 | 1.32 × 10−4 | 2.77 | 1.34 |
25 | 9.97 × 10−6 | 3.73 | 9.97 × 10−6 | 3.73 | 2.64 | 9.97 × 10−6 | 3.73 | 9.96 × 10−6 | 3.73 | 2.65 |
26 | 6.72 × 10−7 | 3.89 | 6.71 × 10−7 | 3.89 | 6.11 | 6.71 × 10−7 | 3.89 | 6.71 × 10−7 | 3.89 | 6.17 |
27 | 7.69 × 10−8 | 3.13 | 7.69 × 10−8 | 3.13 | 12.80 | 7.69 × 10−8 | 3.13 | 7.69 × 10−8 | 3.13 | 13.01 |