Theory and Modern Applications
Table 3 Numerical comparison results of the D-G ADI splitting scheme and the new HOC-ADI splitting scheme for Example 2, 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) |
\(\frac{\pi}{5}\) | 6.790e–2 | – | 23.31 | 9.495e– | – | 36.56 |
\(\frac{\pi}{10}\) | 1.709e–2 | 1.989 | 153.1 | 5.888e–5 | 4.011 | 218.7 |
\(\frac{\pi}{20}\) | 4.281e–3 | 1.997 | 1123.0 | 3.672e–6 | 4.003 | 1547.4 |
\(\frac{\pi}{40}\) | 1.071e–3 | 1.999 | 9307.0 | 2.294e–7 | 4.001 | 12,116.5 |