Theory and Modern Applications
Table 1 Maximum absolute errors for q , u , and J at \(\pmb{N=20}\) , \(\pmb{\alpha =0.3}\) , and various choices of M for Example 5.1
From: A space-time spectral method for the time fractional diffusion optimal control problems
M | 4 | 6 | 8 | 10 | 12 | 14 | 16 |
|---|---|---|---|---|---|---|---|
q | 4.08E − 03 | 5.24E − 05 | 2.93E − 07 | 1.58E − 09 | 9.97E − 12 | 5.17E − 14 | 2.30E − 14 |
u | 4.75E − 02 | 7.96E − 04 | 1.17E − 05 | 1.39E − 07 | 1.28E − 09 | 9.82E − 12 | 3.43E − 13 |
J | 2.86E − 05 | 5.77E − 09 | 8.23E − 13 | 8.83E − 17 | 6.38E − 21 | 3.09E − 25 | 1.12E − 29 |