Table 2 The \(L^{2}\) errors and orders at \(T=0.05\) for v that are computed by BDF1, CN, and BDF2 schemes

0.00500000

4.1100e−05

–

1.8068e−06

–

1.9312e−06

–

0.00250000

2.0715e−05

0.99

4.6180e−07

1.97

4.5096e−07

2.10

0.00125000

1.0399e−05

0.99

1.1654e−07

1.99

1.0960e−07

2.04

0.00062500

5.2100e−06

1.00

2.9259e−08

2.00

2.7044e−08

2.02

0.00031250

2.6076e−06

1.00

7.3294e−09

2.00

6.7187e−09

2.01

0.00015625

1.3045e−06

1.00

1.8341e−09

2.00

1.6745e−09

2.00