Table 5 Numerical errors at \(t=0.5\) in time direction with \(h=1/35\) for \(\lambda =1\).
From: A split-step finite element method for the space-fractional Schrödinger equation in two dimensions
\(\Delta t\) | \(\alpha =0.85\) | \(\alpha =0.95\) | ||||||
|---|---|---|---|---|---|---|---|---|
\(||e_u||_{0,\Omega }\) | Rate | \(||e_v||_{0,\Omega }\) | Rate | \(||e_u||_{0,\Omega }\) | Rate | \(||e_v||_{0,\Omega }\) | Rate | |
1/4 | 2.1993e−05 | – | 7.1209e−06 | – | 2.3573e−05 | – | 6.0014e−06 | – |
1/8 | 6.6032e−06 | 1.74 | 2.4192e−06 | 1.56 | 7.1238e−06 | 1.73 | 1.8461e−06 | 1.70 |
1/16 | 1.8105e−06 | 1.87 | 6.9523e−07 | 1.80 | 1.9158e−06 | 1.89 | 4.9376e−07 | 1.90 |
