Theory and Modern Applications
Table 1 Error, order of accuracy with different values of \(\alpha _{x}\) and \(\alpha _{y}\) for Example 1
\(\alpha _{x}=\alpha _{y}=1.4\) | \(\alpha _{x}=1.4\), \(\alpha _{y}=1.8\) | \(\alpha _{x}=\alpha _{y}=1.8\) | ||||
|---|---|---|---|---|---|---|
\(N_{x}\times N_{y}\) | \(L^{2}\) error | Order | \(L^{2}\) error | Order | \(L^{2}\) error | Order |
16 × 16 | 1.13 × 10−5 | – | 1.18 × 10−5 | – | 1.18 × 10−5 | – |
32 × 32 | 2.75 × 10−6 | 2.02 | 2.86 × 10−6 | 2.03 | 2.85 × 10−6 | 2.03 |
64 × 64 | 6.74 × 10−7 | 2.02 | 7.07 × 10−7 | 2.01 | 7.09 × 10−7 | 2.00 |
128 × 128 | 1.68 × 10−7 | 2.00 | 1.75 × 10−7 | 2.01 | 1.78 × 10−7 | 2.00 |