Theory and Modern Applications
Table 4 Numerical comparison results of schemes CS1DI and CS1DII for Example 2, 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 | 1.020e−3 | – | 2.044e−5 | – |
20 | 3.004e−4 | 1.764 | 2.537e−6 | 3.010 | |
40 | 8.722e−5 | 1.784 | 3.212e−7 | 2.981 | |
80 | 2.506e−5 | 1.800 | 4.115e−8 | 2.965 | |
0.5 | 10 | 0.0154 | – | 9.402e−4 | – |
20 | 5.644e−3 | 1.448 | 1.602e−4 | 2.553 | |
40 | 2.042e−3 | 1.468 | 2.786e−5 | 2.524 | |
80 | 7.330e−4 | 1.478 | 4.886e−6 | 2.511 | |
0.9 | 10 | 0.0889 | – | 0.0156 | – |
20 | 0.0429 | 1.051 | 3.679e−3 | 2.086 | |
40 | 0.0204 | 1.074 | 8.439e−4 | 2.124 | |
80 | 9.588e−3 | 1.087 | 1.968e−4 | 2.100 | |