Table 2 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

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

9.6097e–003

2.1177e–002

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

2.5186e–003

1.9319

5.4063e–003

1.9585

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

6.2591e–004

2.0086

1.2530e–003

2.1574

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

1.5625e–004

2.0021

3.1349e–004

1.9984

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

3.9048e–005

2.0005

7.8366e–005

2.0002

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

9.7610e–006

2.0001

1.9591e–005

2.0001