Theory and Modern Applications
Table 5 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 3, 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 |
|---|---|---|---|---|
\(\frac{1}{4}\) | 1.0256e–004 | 2.0380e-004 | ||
\(\frac{1}{8}\) | 6.7842e–006 | 3.7794 | 1.3093e-005 | 3.8913 |
\(\frac{1}{16}\) | 4.2695e–007 | 3.9724 | 8.4501e-007 | 3.8736 |
\(\frac{1}{32}\) | 2.6719e–008 | 3.9949 | 5.3542e-008 | 3.9456 |
\(\frac{1}{64}\) | 1.6704e–009 | 3.9989 | 3.3473e-009 | 3.9989 |
\(\frac{1}{128}\) | Out of memory | – | Out of memory | – |