Theory and Modern Applications
Table 2 Numerical results of the SHSS-PCG method for solving FDE (\(\alpha =1.5\))
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 | 1456 | Non | 5.1 | 10.8 | 3.4127 | 1.8E − 08 |
T. Chan | 5.1 | 7.2 | 2.4424 | 1.8E − 08 | ||
Strang | 5.1 | 7.3 | 2.4540 | 1.8E − 08 | ||
29 | 4108 | Non | 4.9 | 10.3 | 13.2000 | 6.3E − 08 |
T. Chan | 4.9 | 6.9 | 10.5790 | 6.2E − 08 | ||
Strang | 4.9 | 6.9 | 9.1063 | 6.2E − 08 | ||
210 | 11,602 | Non | 4.9 | 9.9 | 54.7901 | 2.7E − 07 |
T. Chan | 4.9 | 6.4 | 38.3217 | 2.6E − 07 | ||
Strang | 4.9 | 6.4 | 39.2306 | 2.6E − 07 | ||
211 | 32,792 | Non | 4.1 | 9.0 | 222.3530 | 8.5E − 06 |
T. Chan | 4.1 | 5.4 | 158.7036 | 7.8E − 06 | ||
Strang | 4.1 | 5.4 | 151.6013 | 7.8E − 06 |