Table 4 The comparison of the \(l^{2}\)-norm and the \(l^{\infty}\)-norm when \(\tau= h_{x} =h_{y} \) for \(\mathcal{O}(h_{x}^{2} + h_{y}^{2})\) standard central difference scheme, at different values of the step size (for \(N = 4,8,16,32,64,128\)) in the x and y directions

\(\frac{1}{4}\)

3.3066e–006

1.6733e–003

\(\frac{1}{8}\)

8.6085e–007

1.9415

2.2786e–004

3.6718

\(\frac{1}{16}\)

2.1334e–007

2.0126

5.3554e–005

2.1274

\(\frac{1}{32}\)

5.3216e–008

2.0032

1.3026e–005

2.0556

\(\frac{1}{64}\)

1.3297e–008

2.0008

3.2316e–006

2.0154

\(\frac{1}{128}\)

3.3241e–009

2.0000

8.0609e–007

2.0045