Research Article
A Banded Preconditioning Iteration Method for Time-Space Fractional Advection-Diffusion Equations
Table 1
Numerical results of the tested methods for
and
.
| | | S-GMRES | T-GMRES | R-GMRES | (16)-GMRES | (4)-GMRES | IT | CPU | IT | CPU | IT | CPU | IT | CPU | IT | CPU |
| 1.3 | | 18 | 0.18 | 22 | 0.24 | 18 | 0.15 | 8 | 0.07 | 5 | 0.05 | | 20 | 0.51 | 26 | 0.58 | 19 | 0.43 | 8 | 0.18 | 5 | 0.12 | | 21 | 1.60 | 30 | 2.23 | 21 | 1.61 | 8 | 0.63 | 5 | 0.53 | | 22 | 9.12 | 35 | 14.14 | 22 | 9.14 | 8 | 3.02 | 5 | 2.33 | | 23 | 51.10 | 39 | 83.54 | 23 | 51.21 | 8 | 18.57 | 5 | 12.44 | | 23 | 306.29 | 44 | 560.60 | 23 | 307.80 | 8 | 110.39 | 5 | 75.95 | | — | — | — | — | — | — | 8 | 741.27 | 5 | 495.16 |
| 1.6 | | 11 | 0.09 | 18 | 0.17 | 11 | 0.11 | 8 | 0.08 | 4 | 0.06 | | 12 | 0.28 | 22 | 0.46 | 12 | 0.28 | 8 | 0.17 | 4 | 0.11 | | 12 | 0.97 | 26 | 1.93 | 12 | 0.97 | 8 | 0.63 | 4 | 0.43 | | 12 | 5.26 | 30 | 12.11 | 12 | 5.30 | 8 | 3.46 | 4 | 2.32 | | 12 | 28.88 | 36 | 77.01 | 12 | 28.60 | 8 | 18.7 | 4 | 12.4 | | 12 | 169.48 | 43 | 547.79 | 12 | 169.37 | 8 | 109.46 | 4 | 73.25 | | 12 | 1153.13 | — | — | 12 | 1157.55 | 8 | 742.61 | 4 | 496.21 |
| 1.9 | | 8 | 0.08 | 18 | 0.15 | 8 | 0.08 | 6 | 0.06 | 3 | 0.04 | | 8 | 0.19 | 22 | 0.46 | 8 | 0.19 | 6 | 0.14 | 3 | 0.1 | | 8 | 0.71 | 27 | 2.00 | 8 | 0.70 | 6 | 0.49 | 3 | 0.36 | | 8 | 3.79 | 34 | 13.58 | 8 | 3.81 | 6 | 2.71 | 3 | 1.93 | | 8 | 21.18 | 44 | 93.08 | 8 | 20.57 | 6 | 14.45 | 3 | 10.36 | | 8 | 121.58 | 57 | 717.37 | 8 | 121.41 | 6 | 85.41 | 3 | 61.08 | | 7 | 745.34 | — | — | 7 | 742.52 | 6 | 578.17 | 3 | 413.03 |
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