Theory and Modern Applications
Table 2 Numerical comparison results of schemes CS1DI and CS1DII for Example 1, at \(T=1\) with \(N_{x}=2000\) 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 | 1.554e−4 | – | 2.365e−6 | – |
20 | 4.563e−5 | 1.768 | 2.871e−7 | 3.042 | |
40 | 1.322e−5 | 1.787 | 3.538e−8 | 3.021 | |
80 | 3.793e−6 | 1.802 | 4.391e−9 | 3.010 | |
0.5 | 10 | 0.0020 | – | 8.694e−6 | – |
20 | 7.191e−4 | 1.472 | 1.188e−6 | 2.872 | |
40 | 2.577e−4 | 1.480 | 1.830e−7 | 2.699 | |
80 | 9.199e−5 | 1.486 | 3.130e−8 | 2.547 | |
0.9 | 10 | 9.995e−3 | – | 1.334e−3 | – |
20 | 4.699e−3 | 1.089 | 5.067e−4 | 1.397 | |
40 | 2.139e−3 | 1.136 | 1.272e−4 | 1.995 | |
80 | 9.592e−4 | 1.157 | 2.840e−5 | 2.162 | |