Theory and Modern Applications
Table 3 Error, order of accuracy, and CPU time with DC2, cIIF2, and RK2 schemes for Example 2
\(N_{x}\times N_{y}\times N_{z}\) | DC2, \(\Delta t=1/N_{x}=h_{x}/2\pi\) | cIIF2, \(\Delta t=1/N_{x}=h_{x}/2\pi\) | RK2, \(\Delta t=h_{x}^{2}/3\) | ||||||
|---|---|---|---|---|---|---|---|---|---|
\(L^{\infty}\) error | Order | CPU (s) | \(L^{\infty}\) error | Order | CPU (s) | \(L^{\infty}\) error | Order | CPU (s) | |
16 × 16 × 16 | 5.50 × 10−5 | – | 0.05 | 6.95 × 10−3 | – | 0.04 | 6.95 × 10−3 | – | 0.09 |
32 × 32 × 32 | 3.59 × 10−6 | 3.94 | 0.43 | 1.74 × 10−3 | 2.00 | 0.43 | 1.74 × 10−3 | 2.00 | 2.06 |
64 × 64 × 64 | 2.65 × 10−7 | 3.76 | 5.93 | 4.36 × 10−4 | 2.00 | 5.95 | 4.36 × 10−4 | 2.00 | 61.9 |
128 × 128 × 128 | 2.69 × 10−8 | 3.30 | 127 | 1.09 × 10−4 | 2.00 | 124 | 1.09 × 10−4 | 2.00 | 2448 |