Table 4. Reproducing Table 2 from Gao et al. [67] using the Prony-based method Eq. (12) for refinement in space with a constant Δt = 5e–5.
| Gao et al. [67] | Prony approximation | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| N = 3 | N = 6 | N = 9 | N = 12 | |||||||||||||
| α | h | Δt | E(h, Δt) | log2 | E(h, Δt) | log2 | E(h, Δt) | log2 | E(h, Δt) | log2 | E(h, Δt) | log2 | ||||
| 1/2 | 1/10 | 1 /20 000 | 1.50e–2 | 2.00 | 5.95e–3 | 2.06 | 6.02e–3 | 2.01 | 6.02e–3 | 2.01 | 6.01e–3 | 2.01 | ||||
| 1/20 | 3.75e–3 | 2.00 | 1.43e–3 | 2.22 | 1.50e–3 | 2.00 | 1.50e–3 | 2.00 | 1.50e–3 | 2.00 | ||||||
| 1/40 | 9.38e–4 | 2.00 | 3.07e–4 | 3.24 | 3.75e–4 | 1.99 | 3.75e–4 | 1.99 | 3.74e–4 | 2.00 | ||||||
| 1/80 | 2.35e–4 | 2.00 | 3.25e–5 | -0.75 | 9.47e–5 | 1.95 | 9.44e–5 | 1.96 | 9.37e–5 | 2.00 | ||||||
| 1/160 | 5.86e–5 | * | 5.47e–5 | * | 2.45e–5 | * | 2.43e–5 | * | 2.35e–5 | * | ||||||
| 2/3 | 1/10 | 1 /20 000 | 1.37e–2 | 1.99 | 5.67e–3 | 2.08 | 5.77e–3 | 2.00 | 5.77e–3 | 2.00 | 5.77e–3 | 2.00 | ||||
| 1/20 | 3.44e–3 | 2.00 | 1.35e–3 | 2.31 | 1.44e–3 | 1.98 | 1.44e–3 | 1.97 | 1.44e–3 | 1.98 | ||||||
| 1/40 | 8.61e–4 | 2.00 | 2.71e–4 | 3.33 | 3.66e–4 | 1.92 | 3.67e–4 | 1.90 | 3.67e–4 | 1.91 | ||||||
| 1/80 | 2.15e–4 | 2.00 | 2.68e–5 | –1.58 | 9.67e–5 | 1.71 | 9.81e–5 | 1.66 | 9.75e–5 | 1.68 | ||||||
| 1/160 | 5.37e–5 | * | 8.01e–5 | * | 2.96e–5 | * | 3.11e–5 | * | 3.05e–5 | * | ||||||