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Theory and Modern Applications

Table 1 The GPIU algorithm for solving Example 1 with different choices of parameters for \(\alpha =1.5\)

From: A GPIU method for fractional diffusion equations

N

M

(ω, δ, s)

CPU (s)

Iter

Error

26

93

(0.8, 0.8, 0.2)

0.0541

9.85

2.27e − 07

(0.8, 0.9, 0.2)

0.0465

6.97

2.16e − 07

(0.9, 0.9, 0.1)

0.0672

6.98

2.14e − 07

(1, 0.99, 0.01)

0.0432

4

2.72e − 08

(1, 1.1, 0.1)

0.0498

6.98

2.16e − 07

27

259

(0.8, 0.8, 0.2)

0.4028

9.73

5.20e − 07

(0.8, 0.9, 0.2)

0.3590

6.95

5.02e − 07

(0.9, 0.9, 0.1)

0.3599

6.95

5.02e − 07

(1, 0.99, 0.01)

0.3286

3.98

1.73e − 07

(1, 1.1, 0.1)

0.4187

6.95

5.03e − 07

28

728

(0.8, 0.8, 0.2)

3.7215

9.66

1.23e − 06

(0.8, 0.9, 0.2)

3.1373

6.93

1.18e − 06

(0.9, 0.9, 0.1)

3.2618

6.93

1.18e − 06

(1, 0.99, 0.01)

3.4343

3.93

5.68e − 07

(1, 1.1, 0.1)

3.4742

6.93

1.18e − 06

29

2054

(0.8, 0.8, 0.2)

57.9257

9.61

2.96e − 06

(0.8, 0.9, 0.2)

56.3505

6.92

2.78e − 06

(0.9, 0.9, 0.1)

55.5128

6.92

2.78e − 06

(1, 0.99, 0.01)

53.3056

3.92

1.27e − 06

(1, 1.1, 0.1)

56.5414

6.91

2.79e − 06