Research Article
A Numerical Solution to Fractional Diffusion Equation for Force-Free Case
Table 1
The comparison of the exact solutions with the numerical solutions with
,
, and
for different values of
and the error norms
and
.
| | | | | | | Exact |
| 0.0 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.1 | 0.013806 | 0.013886 | 0.013920 | 0.013925 | 0.013926 | 0.013765 | 0.2 | 0.026128 | 0.026284 | 0.026325 | 0.026335 | 0.026336 | 0.026183 | 0.3 | 0.035777 | 0.035982 | 0.036034 | 0.036046 | 0.036048 | 0.036037 | 0.4 | 0.041903 | 0.042137 | 0.042195 | 0.042210 | 0.042212 | 0.042364 | 0.5 | 0.044001 | 0.044245 | 0.044306 | 0.044321 | 0.044323 | 0.044544 | 0.6 | 0.041903 | 0.042137 | 0.042195 | 0.042210 | 0.042212 | 0.042364 | 0.7 | 0.035777 | 0.035982 | 0.036034 | 0.036046 | 0.036048 | 0.036037 | 0.8 | 0.026128 | 0.026284 | 0.026325 | 0.026335 | 0.026336 | 0.026183 | 0.9 | 0.013806 | 0.013886 | 0.013920 | 0.013925 | 0.013926 | 0.013765 | 1.0 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 |
| | 0.294172 | 0.159576 | 0.142246 | 0.139756 | 0.139501 | ā | | 0.543026 | 0.299690 | 0.238942 | 0.223758 | 0.221936 | ā |
|
|