Theory and Modern Applications
Table 6 IVP in Eq. (30). Results for different σ, on domain \(t\in [0,25]\)
From: Adaptive neural-domain refinement for solving time-dependent differential equations
σ | h | \(\Delta \phi _{1}\) | \(E^{\mathrm{VP}}[\mathbf{P}_{m,l}]\) | \(E^{\mathrm{TP}}[\mathbf{P}_{m,l}]\) |
|---|---|---|---|---|
1e-1 | 37 | 5.5512e-2 | 1.8907e-2 | 1.8537e-2 |
1e-2 | 39 | 1.0749e-2 | 1.5714e-3 | 1.6255e-3 |
1e-3 | 47 | 6.2122e-3 | 1.1582e-4 | 1.1917e-4 |
1e-4 | 50 | 6.8152e-4 | 2.6581e-5 | 2.7788e-5 |
1e-5 | 59 | 3.0005e-4 | 1.9260e-6 | 2.2057e-6 |
1e-6 | 74 | 1.1870e-4 | 2.1157e-7 | 2.2076e-7 |