Theory and Modern Applications
Table 9 Maximum residual errors with \(\pmb{n=8}\) for Example 9.3 , the Galerkin 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 | 1.8 | 1.0 × 10−1 | 1.0 × 10−1 | 6.0 × 10−2 | 5.0 × 10−2 | 1.12744 × 10−7 |
0.6 | 8.0 × 10−2 | 6.0 × 10−2 | 2.5 × 10−2 | 2.5 × 10−2 | 3.93491 × 10−7 | |
0.8 | 8.0 × 10−2 | 3.5 × 10−2 | 7.0 × 10−3 | 1.0 × 10−2 | 1.60004 × 10−6 | |
1 | 1.3 | 4.0 × 10−2 | 8.0 × 10−3 | 2.0 × 10−3 | 1.4 × 10−3 | 1.36568 × 10−5 |
1.5 | 6.0 × 10−2 | 8.0 × 10−3 | 4.0 × 10−3 | 8.0 × 10−3 | 2.85066 × 10−5 | |
1.8 | 8.0 × 10−3 | 1.5 × 10−3 | 4.0 × 10−4 | 7.0 × 10−4 | 2.91652 × 10−6 |