Theory and Modern Applications
Table 6 The error comparison between CFDS-PIM and other method with spatial step sizes \({h_{x}} = {h_{y}} = 2.5\times10^{-2}\) and time step size \(\tau= 2 \times{10^{- 5}}\) at \(t=2\) for case 1 of Example 4
CFDS-PIM | Ref. [1] | RK4 | |||
|---|---|---|---|---|---|
Taylor | Padé | ||||
\((x_{i},y_{i})\) | (0.2,0.2) | 8.914 × 10−10 | 9.439 × 10−10 | 4.673 × 10−3 | 8.067 × 10−10 |
(0.4,0.4) | 2.319 × 10−9 | 2.486 × 10−9 | 1.223 × 10−2 | 2.103 × 10−9 | |
(0.6,0.6) | 2.319 × 10−9 | 2.486 × 10−9 | 1.233 × 10−2 | 2.103 × 10−9 | |
(0.8,0.8) | 8.914 × 10−10 | 9.439 × 10−10 | 4.673 × 10−3 | 8.914 × 10−10 | |
CPU (s) | 0.412 | 0.425 | – | 13.869 | |
N | 41 × 41 | 41 × 41 | 101 × 101 | 41 × 41 | |