Theory and Modern Applications
From: A mass-conservative higher-order ADI method for solving unsteady convection–diffusion equations
\(h_{x}=h_{y}\) | τ | Average error | \(L^{\infty }\) norm error | |
---|---|---|---|---|
DHOC-ADI | 0.05 | 0.0125 | 1.99 × 10−3 | 8.98 × 10−3 |
0.00625 | 3.81 × 10−5 | 2.49 × 10−4 | ||
0.025 | 0.0125 | 1.10 × 10−4 | 6.84 × 10−4 | |
0.0001 | 6.17 × 10−7 | 4.98 × 10−6 | ||
HOC-ADI | 0.05 | 0.0125 | 4.48 × 10−4 | 3.32 × 10−3 |
0.00625 | 4.66 × 10−4 | 3.56 × 10−3 | ||
0.025 | 0.0125 | 1.06 × 10−4 | 6.19 × 10−4 | |
0.0001 | 3.07 × 10−5 | 2.43 × 10−4 | ||
EHOC-ADI | 0.05 | 0.0125 | 4.31 × 10−4 | 3.18 × 10−3 |
0.00625 | 4.66 × 10−4 | 3.41 × 10−3 | ||
0.025 | 0.0125 | 1.06 × 10−4 | 6.09 × 10−4 | |
0.0001 | 3.42 × 10−5 | 2.69 × 10−4 | ||
RHOC-ADI | 0.05 | 0.0125 | 2.84 × 10−4 | 2.09 × 10−3 |
0.00625 | 2.88 × 10−4 | 2.19 × 10−3 | ||
0.025 | 0.0125 | 8.39 × 10−5 | 6.54 × 10−4 | |
0.0001 | 9.04 × 10−5 | 7.16 × 10−4 | ||
FTCS | 0.025 | 0.0125 | 3.94 × 10−3 | 1.21 × 10−1 |
Upwind | 0.025 | 0.0125 | 2.65 × 10−3 | 6.63 × 10−1 |
Kalita et al. (9,5) [34] | 0.025 | 0.0125 | 1.49 × 10−3 | 3.74 × 10−2 |
Kalita et al. (5,9) [34] | 0.025 | 0.0125 | 1.02 × 10−3 | 2.25 × 10−2 |
Kalita et al. (9,9) [34] | 0.025 | 0.0125 | 5.24 × 10−5 | 1.19 × 10−3 |
Kalita et al. [35] | 0.025 | 0.0125 | 7.77 × 10−5 | 1.69 × 10−3 |
Noye and Tan [33] | 0.025 | 0.0125 | 1.43 × 10−5 | 4.84 × 10−4 |