Theory and Modern Applications
Table 3 The comparison of the \(l^{2}\)-norm and the \(l^{\infty}\)-norm when \(\tau^{2} = h_{x} =h_{y} \) for \(\mathcal{O}(h_{x}^{4} + h_{y}^{4})\) fourth-order compact finite difference schemes in Example 2, at different values of the step size (for \(N = 4,8,16,32,64,128\)) in the x and y directions
h | \(\mathrm{err}L^{2}\) | order | \(\mathrm{err}L^{\infty}\) | order |
|---|---|---|---|---|
\(\frac{1}{4}\) | 6.1733e–006 | 1.1640e–005 | ||
\(\frac{1}{8}\) | 3.8740e–007 | 3.9838 | 7.2789e–007 | 3.9979 |
\(\frac{1}{16}\) | 2.4219e–008 | 3.9990 | 4.5494e–008 | 3.9999 |
\(\frac{1}{32}\) | 1.5137e–009 | 3.9999 | 2.8434e–009 | 4.0000 |
\(\frac{1}{64}\) | 9.4606e–0011 | 4.0000 | 1.7771e–0010 | 4.0000 |
\(\frac{1}{128}\) | Out of memory | – | Out of memory | – |