Theory and Modern Applications
Table 1 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 1, 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 |
|---|---|---|---|---|
\(\frac{1}{4}\) | 3.1833e–004 | 6.3680e–004 | ||
\(\frac{1}{8}\) | 2.0323e–005 | 3.9158 | 4.0654e–005 | 3.9160 |
\(\frac{1}{16}\) | 1.2761e–006 | 3.9815 | 1.6045e–007 | 3.9815 |
\(\frac{1}{32}\) | 7.9847e–008 | 3.9955 | 1.6045e–007 | 3.9772 |
\(\frac{1}{64}\) | 4.9917e–009 | 3.9989 | 1.0031e–008 | 3.9989 |
\(\frac{1}{128}\) | Out of memory | – | Out of memory | – |