Theory and Modern Applications
Table 2 Comparison of maximum errors at different time T for the equation in Example 1, \(h=2\pi/20\), time step \(\tau=0.01\)
From: A new high-order compact ADI finite difference scheme for solving 3D nonlinear Schrödinger equation
D-G ADI scheme | New HOC-ADI scheme | |||
|---|---|---|---|---|
T | Error | CPU(s) | Error | CPU(s) |
0.5 | 1.230e–2 | 1.45 | 6.112e–5 | 2.54 |
1 | 2.459e–2 | 2.84 | 1.222e–4 | 4.92 |
2 | 4.918e–2 | 5.55 | 2.445e–4 | 10.0 |
3 | 7.376e–2 | 8.42 | 3.667e–4 | 15.1 |
4 | 9.833e–2 | 10.5 | 4.890e–4 | 20.4 |