Table 3 Numerical errors at \(t=0.5\) in time direction with \(h=1/35\) for \(\lambda =0\).
From: A split-step finite element method for the space-fractional Schrödinger equation in two dimensions
\(\Delta t\) | \(\alpha =0.8\) | \(\alpha =0.9\) | ||||||
|---|---|---|---|---|---|---|---|---|
\(||e_u||_{0,\Omega }\) | Rate | \(||e_v||_{0,\Omega }\) | Rate | \(||e_u||_{0,\Omega }\) | Rate | \(||e_v||_{0,\Omega }\) | Rate | |
1/4 | 1.3492e−05 | – | 1.8760e−05 | – | 1.5446e−05 | – | 1.8931e−05 | – |
1/8 | 3.3610e−06 | 2.01 | 5.8009e−06 | 1.69 | 4.0101e−06 | 1.95 | 5.8518e−06 | 1.69 |
1/16 | 8.8615e−07 | 1.92 | 1.6163e−06 | 1.84 | 1.0603e−06 | 1.92 | 1.5997e−06 | 1.87 |
