Theory and Modern Applications
Table 5 Maximum residual errors for \(\pmb{n=8}\) for Example 9.2 , the collocation method
From: Normalized Bernstein polynomials in solving space-time fractional diffusion equation
β | α | T  = 2 | T  = 10 | T  = 50 | T  = 100 | \(\boldsymbol{R_{\infty}}\) |
|---|---|---|---|---|---|---|
0.4 | 2 | 8.0 × 10−3 | 1.4 × 10−2 | 7.0 × 10−3 | 5.0 × 10−3 | 2.64548 × 10−8 |
0.6 | 3.0 × 10−3 | 6.0 × 10−3 | 2.0 × 10−3 | 1.5 × 10−3 | 2.57232 × 10−8 | |
0.8 | 5.0 × 10−3 | 2.0 × 10−3 | 5.0 × 10−4 | 3.0 × 10−4 | 2.85507 × 10−8 | |
1 | 1.4 | 6.0 × 10−2 | 1.5 × 10−2 | 2.5 × 10−3 | 5.0 × 10−5 | 9.5567 × 10−8 |
1.6 | 2.0 × 10−2 | 2.5 × 10−3 | 4.0 × 10−4 | 5.0 × 10−6 | 4.49503 × 10−8 | |
1.8 | 1.5 × 10−4 | 1.5 × 10−4 | 2.0 × 10−5 | 1.2 × 10−7 | 3.52396 × 10−8 |