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Theory and Modern Applications

Table 6 Comparison errors at \(T=1.25\) with different \(h_{x}\), \(h_{y}\), and τ

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