Theory and Modern Applications
Table 1 The error norms of numerical solutions and the rate of convergence in space where \(\tau =0.0001\)
From: A mass-conservative higher-order ADI method for solving unsteady convection–diffusion equations
h | \(L^{2} \) error norm | Rate | \(L^{\infty }\) error norm | Rate | |
|---|---|---|---|---|---|
DHOC-ADI | 0.8 | 1.83952 × 10−3 | – | 1.04192 × 10−3 | – |
0.4 | 3.29634 × 10−5 | 5.80232 | 1.93998 × 10−5 | 5.74705 | |
0.2 | 5.22365 × 10−7 | 5.97966 | 3.08672 × 10−7 | 5.97382 | |
0.1 | 8.12295 × 10−9 | 6.00691 | 4.79173 × 10−9 | 6.00938 | |
HOC-ADI [14] | 0.8 | 1.52825 × 10−2 | – | 8.55117 × 10−3 | – |
0.4 | 1.04708 × 10−3 | 3.86744 | 6.11681 × 10−4 | 3.80527 | |
0.2 | 6.58088 × 10−5 | 3.99194 | 3.87684 × 10−5 | 3.97983 | |
0.1 | 4.11305 × 10−6 | 4.00000 | 2.42285 × 10−6 | 4.00011 | |
EHOC-ADI [16] | 0.8 | 1.21641 × 10−2 | – | 6.56784 × 10−3 | – |
0.4 | 1.07036 × 10−3 | 3.50660 | 6.25626 × 10−4 | 3.39207 | |
0.2 | 7.51890 × 10−5 | 3.83129 | 4.42441 × 10−5 | 3.82172 | |
0.1 | 4.85407 × 10−6 | 3.95328 | 2.85767 × 10−6 | 3.95263 | |
RHOC ADI [17] | 0.8 | 2.46040 × 10−3 | – | 1.42352 × 10−3 | – |
0.4 | 1.35129 × 10−3 | 0.86456 | 7.91705 × 10−4 | 0.84643 | |
0.2 | 1.90001 × 10−4 | 2.83025 | 1.11645 × 10−4 | 2.82604 | |
0.1 | 9.20647 × 10−6 | 4.36722 | 5.41556 × 10−6 | 4.36567 |