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Theory and Modern Applications

Table 3 Numerical results of the SHSS-PCG method for solving FDE (\(\alpha =1.8\))

From: On single-step HSS iterative method with circulant preconditioner for fractional diffusion equations

N + 1

M

Pre.

\(\mathrm{IT} _{\mathrm{SHSS}}\)

\(\mathrm{IT} _{\mathrm{PCG}}\)

CPU (s)

ERR

28

6252

Non

4.0

9.5

10.4430

8.7E − 07

T. Chan

4.0

5.3

6.3253

8.7E − 07

Strang

4.0

5.1

6.0853

8.7E − 07

29

21,694

Non

4.0

8.6

44.4843

3.1E − 06

T. Chan

4.0

4.6

26.9088

3.1E − 06

Strang

4.0

4.6

26.8528

3.1E − 05

210

75,413

Non

4.0

7.6

230.6453

1.1E − 05

T. Chan

4.0

4.0

140.1736

1.1E − 05

Strang

4.0

4.0

141.2357

1.1E − 05

211

262,374

Non

4.0

6.4

1324.4353

3.7E − 05

T. Chan

4.0

3.8

888.2863

3.7E − 05

Strang

4.0

3.8

899.8794

3.7E − 05