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

1/5

1.2615e − 03

2.2800e − 03

5.8869e − 04

8.2114e + 04

1/10

3.1440e − 04

5.6825e − 04

1.4672e − 04

7.8243e + 04

1/20

7.8540e − 05

1.4195e − 04

3.6652e − 05

7.6307e + 04

1/40

1.9631e − 05

3.5481e − 05

9.1613e − 06

7.5340e + 04

1/80

4.9076e − 06

8.8699e − 06

2.2902e − 06

7.4856e + 04

1/160

1.2269e − 06

2.2175e − 06

5.7254e − 07

7.4614e + 04

1/320

3.0672e − 07

5.5436e − 07

1.4314e − 07

7.4493e + 04

1/640

7.6680e − 08

1.3859e − 07

3.5784e − 08

7.4433e + 04

1/1280

1.9170e − 08

3.4647e − 08

8.9457e − 09

7.4402e + 04

1/2560

4.7868e − 09

8.6517e − 09

2.2339e − 09

7.4387e + 04

1/5120

1.2030e − 09

2.1718e − 09

5.6076e − 10

7.4380e + 04