Theory and Modern Applications
Table 2 Error and order of convergence of spatial discretization for example 1
From: Solution of two-dimensional time-fractional Burgers equation with high and low Reynolds numbers
h | α  = 0.7 | α  = 0.8 | α  = 0.9 | |||
|---|---|---|---|---|---|---|
\(\boldsymbol {\Vert e_{u} \Vert _{2}}\) | Order | \(\boldsymbol {\Vert e_{u} \Vert _{2}}\) | Order | \(\boldsymbol { \Vert e_{u} \Vert _{2}}\) | Order | |
|  | N = 1 | |||||
0.4 | 4.43e–02 |  | 4.29e–02 |  | 4.1e–2 | - |
0.2 | 9.89e–03 | 2.16 | 9.80e–03 | 2.13 | 9.8e–3 | 2.06 |
0.1 | 2.37e–03 | 2.06 | 2.35e–03 | 2.06 | 2.3e–3 | 2.09 |
|  | N = 2 | |||||
0.8 | 7.78e–02 |  | 7.08e–02 |  | 6.45e–02 |  |
0.4 | 1.19e–02 | 2.71 | 1.13e–02 | 2.65 | 1.07e–02 | 2.59 |
0.2 | 1.39e–03 | 3.10 | 1.40e–03 | 3.01 | 1.30e–03 | 3.04 |