Theory and Modern Applications
Table 2 Spatial convergence rate for Example 2 with fixed \(h=0.00002\)
From: Numerical solution of advection–diffusion type equation by modified error correction scheme
\(M_{x}=M_{y}\) | t = 0.1 | t = 1.0 | ||||||
|---|---|---|---|---|---|---|---|---|
\(\mathit {err}_{\infty }(t)\) | Rates | \(\mathit {err}_{R2}(t)\) | Rates | \(\mathit {err}_{\infty }(t)\) | Rates | \(\mathit {err}_{R2}(t)\) | Rates | |
ν = 0.1 | ||||||||
20 | 7.45 × 10−6 | – | 7.81 × 10−6 | – | 2.11 × 10−5 | – | 1.30 × 10−5 | – |
40 | 1.36 × 10−7 | 5.78 | 3.28 × 10−7 | 4.58 | 1.31 × 10−6 | 4.02 | 8.67 × 10−7 | 3.90 |
80 | 1.33 × 10−8 | 3.36 | 2.47 × 10−8 | 3.73 | 8.16 × 10−8 | 4.00 | 5.51 × 10−8 | 3.98 |
160 | 9.59 × 10−10 | 3.79 | 1.64 × 10−9 | 3.91 | 5.24 × 10−9 | 3.96 | 3.58 × 10−9 | 3.94 |
320 | 9.00 × 10−11 | 3.41 | 1.67 × 10−10 | 3.30 | 5.05 × 10−10 | 3.38 | 3.60 × 10−10 | 3.31 |
ν = 0.01 | ||||||||
40 | 4.04 × 10−2 | – | 2.16 × 10−2 | – | 2.63 × 10−2 | – | 3.13 × 10−3 | – |
80 | 5.90 × 10−4 | 6.10 | 3.84 × 10−4 | 5.81 | 8.02 × 10−4 | 5.03 | 2.07 × 10−4 | 3.92 |
160 | 5.06 × 10−5 | 3.54 | 3.00 × 10−5 | 3.68 | 5.51 × 10−5 | 3.86 | 1.35 × 10−5 | 3.94 |
320 | 3.18 × 10−6 | 3.99 | 2.08 × 10−6 | 3.85 | 3.39 × 10−6 | 4.02 | 8.58 × 10−7 | 3.98 |
640 | 1.98 × 10−7 | 4.01 | 1.33 × 10−7 | 3.96 | 2.28 × 10−7 | 3.90 | 5.99 × 10−8 | 3.84 |