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Theory and Modern Applications

Table 5 Errors and convergence orders of schemes CS2DI and CS2DII for Example 3, at \(T=1\) with different α, M, and N

From: On high-order compact schemes for the multidimensional time-fractional Schrödinger equation

α

M

N

Scheme CS2DI

Scheme CS2DII

\(L^{\infty }\)-error

Order

\(L^{\infty }\)-error

Order

0.25

5

50

5.328e−3

5.277e−3

10

460

3.587e−4

3.893

3.552e−4

3.892

20

4222

2.247e−5

3.997

2.226e−5

3.996

0.5

5

50

1.935e−3

1.911e−3

10

317

1.309e−4

3.885

1.293e−4

3.885

20

2016

8.175e−6

4.002

8.075e−6

4.002

0.75

50

50

7.654e−4

7.580e−4

10

244

5.351e−5

3.838

5.289e−5

3.841

20

1189

3.614e−6

3.888

3.558e−6

3.894