Theory and Modern Applications
Table 3 Numerical comparison results of schemes CS1DI and CS1DII for Example 2, 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 | 0.0218 | – | 0.0218 | – |
8 | 1.277e−3 | 4.094 | 1.277e−3 | 4.093 | |
16 | 7.812e−5 | 4.031 | 7.841e−5 | 4.026 | |
32 | 4.823e−6 | 4.018 | 4.906e−6 | 3.999 | |
0.5 | 4 | 0.0181 | – | 0.0181 | – |
8 | 1.056e−3 | 4.096 | 1.062e−3 | 4.089 | |
16 | 6.186e−5 | 4.094 | 6.624e−5 | 4.003 | |
32 | 3.860e−6 | 4.002 | 4.138e−6 | 4.001 | |