Theory and Modern Applications
Table 1 Numerical comparison results of schemes CS1DI and CS1DII for Example 1, at \(T=1\) with \(N=1000\) and different \(N_{x}\) and α
From: On high-order compact schemes for the multidimensional time-fractional Schrödinger equation
α | \(N_{x}\) | Scheme CS1DI | Scheme CS1DII | ||
|---|---|---|---|---|---|
\(L^{\infty }\)-error | Order | \(L^{\infty }\)-error | Order | ||
0.25 | 4 | 0.0394 | – | 0.0394 | – |
8 | 2.281e−3 | 4.111 | 2.281e−3 | 4.111 | |
16 | 1.399e−4 | 4.027 | 1.400e−4 | 4.027 | |
32 | 8.700e−6 | 4.008 | 8.707e−6 | 4.007 | |
0.5 | 4 | 0.0393 | – | 0.0393 | – |
8 | 2.278e−3 | 4.111 | 2.278e−3 | 4.110 | |
16 | 1.396e−4 | 4.029 | 1.397e−4 | 4.027 | |
32 | 8.752e−6 | 3.995 | 8.694e−6 | 4.007 | |