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Theory and Modern Applications

Table 1 The global maximum \(\pmb{H_{0}^{1}}\) -errors \(\pmb{\max_{0\leq n\leq N} \|u^{n}-u_{h}^{n}\|_{H_{0}^{1}}}\) for equation ( 42 ) with \(\pmb{h = \pi/256}\)

From: An alternating direction Galerkin method for a time-fractional partial differential equation with damping in two space dimensions

α

N

8

16

32

64

128

1.35

5.071E-02

1.391E-02

3.650E-03

9.374E-04

2.381E-04

-

1.8661

1.9303

1.9612

1.9771

1.55

3.522E-02

9.681E-03

2.550E-03

6.578E-04

1.677E-04

-

1.8631

1.9245

1.9549

1.9715

1.75

1.992E-02

5.513E-03

1.466E-03

3.825E-04

9.864E-05

-

1.8535

1.9105

1.9388

1.9551