Theory and Modern Applications
Table 1 Temporal convergence rate for Example 2
From: Numerical solution of advection–diffusion type equation by modified error correction scheme
h | 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, \(\Delta x=\Delta y=\frac{1}{2000}\) | ||||||||
\(\frac{1}{50}\) | 3.23 × 10−4 | – | 2.37 × 10−4 | – | 5.56 × 10−4 | – | 5.01 × 10−4 | – |
\(\frac{1}{100}\) | 9.00 × 10−5 | 1.84 | 6.61 × 10−5 | 1.84 | 1.44 × 10−4 | 1.94 | 1.32 × 10−4 | 1.92 |
\(\frac{1}{200}\) | 2.38 × 10−5 | 1.92 | 1.74 × 10−5 | 1.92 | 3.68 × 10−5 | 1.97 | 3.39 × 10−5 | 1.96 |
\(\frac{1}{400}\) | 6.28 × 10−6 | 1.92 | 4.39 × 10−6 | 1.99 | 9.29 × 10−6 | 1.99 | 8.57 × 10−6 | 1.98 |
\(\frac{1}{800}\) | 1.12 × 10−6 | 2.49 | 1.28 × 10−6 | 1.78 | 2.21 × 10−6 | 2.07 | 2.01 × 10−6 | 2.09 |
ν = 0.01, \(\Delta x=\Delta y=\frac{1}{2000}\) | ||||||||
\(\frac{1}{50}\) | 5.91 × 10−2 | – | 3.29 × 10−2 | – | 3.37 × 10−1 | – | 7.08 × 10−2 | – |
\(\frac{1}{100}\) | 1.17 × 10−2 | 2.34 | 8.81 × 10−2 | 1.90 | 2.12 × 10−2 | 3.99 | 5.18 × 10−3 | 3.77 |
\(\frac{1}{200}\) | 3.16 × 10−3 | 1.89 | 2.68 × 10−3 | 1.72 | 3.81 × 10−3 | 2.48 | 1.08 × 10−3 | 2.26 |
\(\frac{1}{400}\) | 8.54 × 10−4 | 1.89 | 7.59 × 10−4 | 1.82 | 9.46 × 10−4 | 2.01 | 2.84 × 10−4 | 1.93 |
\(\frac{1}{800}\) | 2.12 × 10−4 | 2.01 | 1.90 × 10−4 | 2.00 | 2.34 × 10−5 | 2.02 | 7.02 × 10−5 | 2.01 |