Theory and Modern Applications
Table 1 Error, order of accuracy, and CPU time with DC2, cIIF2, and RK2 schemes for Example 1
\(N_{x}\times N_{y}\) | DC2, \(\Delta t=1/N_{x}=h_{x}/2\pi\) | cIIF2, \(\Delta t=1/N_{x}=h_{x}/2\pi\) | RK2, \(\Delta t=h_{x}^{2}\) | ||||||
|---|---|---|---|---|---|---|---|---|---|
\(L^{\infty}\) error | Order | CPU (s) | \(L^{\infty}\) error | Order | CPU (s) | \(L^{\infty}\) error | Order | CPU (s) | |
32 × 32 | 2.39 × 10−6 | – | 0.00 | 1.16 × 10−3 | – | 0.00 | 1.16 × 10−3 | – | 0.00 |
64 × 64 | 1.77 × 10−7 | 3.76 | 0.03 | 2.91 × 10−4 | 2.00 | 0.03 | 2.91 × 10−4 | 2.00 | 0.07 |
128 × 128 | 1.80 × 10−8 | 3.30 | 0.37 | 7.27 × 10−5 | 2.00 | 0.37 | 7.27 × 10−5 | 2.00 | 2.20 |
256 × 256 | 2.85 × 10−9 | 2.66 | 5.71 | 1.82 × 10−5 | 2.00 | 5.68 | 1.82 × 10−5 | 2.00 | 70.5 |