Theory and Modern Applications
Table 1 Numerical comparison results of the D-G ADI scheme and the new HOC-ADI scheme for Example 1, at \(T=2\), time step \(\tau=0.001\)
From: A new high-order compact ADI finite difference scheme for solving 3D nonlinear Schrödinger equation
D-G ADI scheme | New HOC-ADI scheme | |||||
|---|---|---|---|---|---|---|
h | Error | Order | CPU(s) | Error | Order | CPU(s) |
\(\frac{\pi}{5}\) | 0.167 | – | 9.750 | 3.403e-3 | – | 20.68 |
\(\frac{\pi}{10}\) | 4.918e–2 | 1.766 | 65.58 | 2.445e–4 | 3.799 | 124.0 |
\(\frac{\pi}{20}\) | 1.233e–2 | 1.996 | 475.8 | 1.524e–5 | 4.004 | 848.0 |
\(\frac{\pi}{40}\) | 3.084e–3 | 1.999 | 3882.8 | 9.515e–7 | 4.001 | 6020.7 |