Table 4 Numerical errors at \(t=0.5\) in space direction with \(\Delta t=2.0e-04\) for \(\lambda =0\).
From: A split-step finite element method for the space-fractional Schrödinger equation in two dimensions
h | \(\alpha =0.8\) | \(\alpha =0.9\) | ||||||
|---|---|---|---|---|---|---|---|---|
\(||e_u||_{0,\Omega }\) | Rate | \(||e_v||_{0,\Omega }\) | Rate | \(||e_u||_{0,\Omega }\) | Rate | \(||e_v||_{0,\Omega }\) | Rate | |
1/5 | 4.8177e−06 | – | 5.8883e−06 | – | 5.3680e−06 | – | 6.0798e−06 | – |
1/10 | 1.2246e−06 | 1.98 | 1.5138e−06 | 1.96 | 1.3627e−06 | 1.98 | 1.5616e−06 | 1.96 |
1/20 | 3.1451e−07 | 1.96 | 4.0251e−07 | 1.91 | 3.3456e−07 | 2.03 | 3.8652e−07 | 2.01 |
