Theory and Modern Applications
Table 6 Numerical comparison results of schemes CS2DI and CS2DII for Example 3, at \(T=1\) with \(M=100\) and different N and α
From: On high-order compact schemes for the multidimensional time-fractional Schrödinger equation
α | N | Scheme CS1DI | Scheme CS1DII | ||
|---|---|---|---|---|---|
\(L^{\infty }\)-error | Order | \(L^{\infty }\)-error | Order | ||
0.1 | 10 | 6.742e−2 | – | 6.735e−2 | – |
20 | 3.129e−2 | 1.107 | 3.111e−2 | 1.114 | |
40 | 1.393e−2 | 1.168 | 1.385e−2 | 1.168 | |
80 | 6.438e−3 | 1.114 | 6.404e−3 | 1.113 | |
0.5 | 10 | 2.181e−2 | – | 2.141e−2 | – |
20 | 8.062e−3 | 1.436 | 7.964e−3 | 1.427 | |
40 | 2.886e−3 | 1.482 | 2.850e−3 | 1.482 | |
80 | 1.028e−3 | 1.489 | 1.015e−3 | 1.489 | |
0.9 | 10 | 9.789e−3 | – | 9.750e−3 | – |
20 | 2.759e−3 | 1.827 | 2.747e−3 | 1.828 | |
40 | 7.797e−4 | 1.823 | 7.757e−4 | 1.824 | |
80 | 2.243e−4 | 1.798 | 2.229e−4 | 1.799 | |