Table 1 The \(L^{2}\) errors and orders at \(T=0.05\) for u that are computed by BDF1, CN, and BDF2 schemes
δt | BDF1 | Order | CN | Order | BDF2 | Order |
|---|---|---|---|---|---|---|
0.00500000 | 1.1251e−04 | – | 1.1339e−05 | – | 1.7578e−05 | – |
0.00250000 | 5.6168e−05 | 1.00 | 2.8323e−06 | 2.00 | 4.4314e−06 | 1.99 |
0.00125000 | 2.8061e−05 | 1.00 | 7.0745e−07 | 2.00 | 1.1121e−06 | 1.99 |
0.00062500 | 1.4025e−05 | 1.00 | 1.7676e−07 | 2.00 | 2.7854e−07 | 2.00 |
0.00031250 | 7.0109e−06 | 1.00 | 4.4176e−08 | 2.00 | 6.9696e−08 | 2.00 |
0.00015625 | 3.5051e−06 | 1.00 | 1.1042e−08 | 2.00 | 1.7432e−08 | 2.00 |