Theory and Modern Applications
Table 1 Numerical results of the SHSS-PCG method for solving FDE (\(\alpha =1.2\))
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 | 339 | Non | 7.5 | 10.3 | 1.1352 | 2.1E − 08 |
T. Chan | 7.5 | 7.1 | 0.8362 | 2.1E − 08 | ||
Strang | 7.5 | 7.1 | 0.8148 | 2.1E − 08 | ||
29 | 777 | Non | 7.2 | 10.2 | 3.3909 | 1.7E − 08 |
T. Chan | 7.2 | 7.1 | 2.5087 | 1.7E − 08 | ||
Strang | 7.2 | 7.1 | 2.5267 | 1.7E − 08 | ||
210 | 1784 | Non | 6.6 | 10.1 | 11.6483 | 7.0E − 08 |
T. Chan | 6.6 | 7.0 | 8.6258 | 7.2E − 08 | ||
Strang | 6.6 | 7.0 | 8.8675 | 7.3E − 08 | ||
211 | 4098 | Non | 6.5 | 9.8 | 48.6901 | 1.2E − 07 |
T. Chan | 6.5 | 6.8 | 36.0236 | 1.5E − 07 | ||
Strang | 6.5 | 6.8 | 35.4271 | 1.5E − 07 |