Theory and Modern Applications
Table 2 The error norms of numerical solutions and the rate of convergence in time where \(h=0.01\)
From: A mass-conservative higher-order ADI method for solving unsteady convection–diffusion equations
τ | \(L^{2} \) error norm | Rate | \(L^{\infty }\) error norm | Rate | |
|---|---|---|---|---|---|
DHOC-ADI | 0.1 | 4.72724 × 10−4 | – | 2.40082 × 10−4 | – |
0.05 | 1.18218 × 10−4 | 1.99955 | 6.00246 × 10−5 | 1.99990 | |
0.025 | 2.95567 × 10−5 | 1.99989 | 1.50064 × 10−5 | 1.99998 | |
0.0125 | 7.38933 × 10−6 | 1.99997 | 3.75162 × 10−6 | 1.99999 | |
HOC-ADI [14] | 0.1 | 4.72724 × 10−4 | – | 2.40082 × 10−4 | – |
0.05 | 1.18218 × 10−4 | 1.99955 | 6.00246 × 10−5 | 1.99990 | |
0.025 | 2.95567 × 10−5 | 1.99989 | 1.50064 × 10−5 | 1.99998 | |
0.0125 | 7.38927 × 10−6 | 1.99998 | 3.75159 × 10−6 | 2.00000 | |
EHOC-ADI [16] | 0.1 | 4.72724 × 10−4 | – | 2.40082 × 10−4 | – |
0.05 | 1.18218 × 10−4 | 1.99955 | 6.00246 × 10−5 | 1.99990 | |
0.025 | 2.95567 × 10−5 | 1.99989 | 1.50064 × 10−5 | 1.99998 | |
0.0125 | 7.38925 × 10−6 | 1.99998 | 3.75157 × 10−6 | 2.00001 | |
RHOC-ADI [17] | 0.1 | 4.72724 × 10−4 | – | 2.40082 × 10−4 | – |
0.05 | 1.18218 × 10−4 | 1.99955 | 6.00246 × 10−5 | 1.99990 | |
0.025 | 2.95566 × 10−5 | 1.99989 | 1.50063 × 10−5 | 1.99998 | |
0.0125 | 7.38915 × 10−6 | 2.00000 | 3.75151 × 10−6 | 2.00003 |