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Theory and Modern Applications

Table 3 Comparing results to solve Example 2 by the GPIU algorithm with \(\omega =1\), \(\delta =0.99\) and \(s = 0.01\), and the CGNR method for \(\alpha =1.2\), 1.5 and 1.8

From: A GPIU method for fractional diffusion equations

α

N

M

GPUI

CGNR

HSS

CPU (s)

Iter

Error

CPU (s)

Iter

Error

CPU (s)

Iter

Error

1.2

26

33

0.0419

5.5152

3.55e − 06

0.2310

65

1.71e − 05

0.0815

16

1.05e − 05

27

74

0.1142

5.04

4.19e − 06

0.7962

77

2.58e − 05

0.5448

22

3.36e − 05

28

170

0.8816

5.01

3.35e − 06

3.4947

81

2.46e − 05

4.1474

22

7.78e − 05

29

389

9.7131

4.12

1.85e − 05

60.4473

82

2.51e − 04

63.5913

22

1.77e − 04

1.5

26

93

0.0561

4.98

6.10e − 07

0.5494

70

2.49e − 05

0.2148

24

1.83e − 05

27

259

0.3715

4.04

5.30e − 06

2.8837

84

1.98e − 04

1.6499

24

5.11e − 05

28

728

3.1912

4

3.88e − 06

16.7189

88

2.32e − 04

18.1177

24

1.28e − 04

29

2054

53.8474

4.00

6.35e − 06

312.7302

89

2.35e − 04

342.1307

24

3.09e − 04

1.8

26

263

0.1348

4.00

5.37e − 07

1.6771

78

1.51e − 05

0.6147

27

2.49e − 05

27

904

1.1877

3.99

3.17e − 06

11.4262

98

2.33e − 05

5.4371

27

6.98e − 05

28

3126

13.6965

3.98

1.43e − 05

81.1444

103

2.46e − 04

73.2352

27

1.88e − 04