Table 4 Error norms and associated condition number \(\kappa (\mathbf{{A}})\) of Example 2 when \(N=225\), \(M=25\) and \(T=1\) at various time steps

1/5

1.3814e − 03

2.4306e − 03

6.2759e − 04

9.2470e + 04

1/10

3.4428e − 04

6.0579e − 04

1.5641e − 04

8.8109e + 04

1/20

8.6003e − 05

1.5133e − 04

2.1317e − 06

8.5929e + 04

1/40

2.1497e − 05

3.7826e − 05

9.7665e − 06

8.4839e + 04

1/80

5.3739e − 06

9.4559e − 06

2.4415e − 06

8.4294e + 04

1/160

1.3435e − 06

2.3640e − 06

6.1037e − 07

8.4022e + 04

1/320

3.3586e − 07

5.9099e − 07

1.5259e − 07

8.3885e + 04

1/640

8.3968e − 08

1.4775e − 07

3.8149e − 08

8.3817e + 04

1/1280

2.0991e − 08

3.6936e − 08

9.5369e − 09

8.3783e + 04

1/2560

5.2518e − 09

9.2389e − 09

2.3855e − 09

8.3766e + 04

1/5120

1.3134e − 09

2.3077e − 09

5.9584e − 10

8.3758e + 04