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Theory and Modern Applications

Table 7 Quantities \(Q^{n}\) under different step sizes \(h_{x}\), \(h_{y}\), and τ at various time

From: A mass-conservative higher-order ADI method for solving unsteady convection–diffusion equations

t

\(h_{x}=h_{y}=0.01\), τ = 0.0125

\(h_{x}=h_{y}=0.05\), τ = 2.5 × 10−6

\(Q^{n}\)

\(|Q^{n}-Q(0)|\)

\(Q^{n}\)

\(|Q^{n}-Q(0)|\)

0

0.0314159265

0.0314159265

0.25

0.0314159265

1.36696 × 10−15

0.0314159265

1.00833 × 10−12

0.50

0.0314159265

2.27596 × 10−15

0.0314159265

2.06732 × 10−12

0.75

0.0314159265

2.65066 × 10−15

0.0314159265

3.13927 × 10−12

1.00

0.0314159265

4.42701 × 10−15

0.0314159265

4.20146 × 10−12

1.25

0.0314159265

5.66908 × 10−15

0.0314159265

5.24557 × 10−12