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Table 1 Temporal convergence rate for Example 2

From: Numerical solution of advection–diffusion type equation by modified error correction scheme

h t = 0.1 t = 1.0
\(\mathit {err}_{\infty }(t)\) Rates \(\mathit {err}_{R2}(t)\) Rates \(\mathit {err}_{\infty }(t)\) Rates \(\mathit {err}_{R2}(t)\) Rates
ν = 0.1, \(\Delta x=\Delta y=\frac{1}{2000}\)
\(\frac{1}{50}\) 3.23 × 10−4 2.37 × 10−4 5.56 × 10−4 5.01 × 10−4
\(\frac{1}{100}\) 9.00 × 10−5 1.84 6.61 × 10−5 1.84 1.44 × 10−4 1.94 1.32 × 10−4 1.92
\(\frac{1}{200}\) 2.38 × 10−5 1.92 1.74 × 10−5 1.92 3.68 × 10−5 1.97 3.39 × 10−5 1.96
\(\frac{1}{400}\) 6.28 × 10−6 1.92 4.39 × 10−6 1.99 9.29 × 10−6 1.99 8.57 × 10−6 1.98
\(\frac{1}{800}\) 1.12 × 10−6 2.49 1.28 × 10−6 1.78 2.21 × 10−6 2.07 2.01 × 10−6 2.09
ν = 0.01, \(\Delta x=\Delta y=\frac{1}{2000}\)
\(\frac{1}{50}\) 5.91 × 10−2 3.29 × 10−2 3.37 × 10−1 7.08 × 10−2
\(\frac{1}{100}\) 1.17 × 10−2 2.34 8.81 × 10−2 1.90 2.12 × 10−2 3.99 5.18 × 10−3 3.77
\(\frac{1}{200}\) 3.16 × 10−3 1.89 2.68 × 10−3 1.72 3.81 × 10−3 2.48 1.08 × 10−3 2.26
\(\frac{1}{400}\) 8.54 × 10−4 1.89 7.59 × 10−4 1.82 9.46 × 10−4 2.01 2.84 × 10−4 1.93
\(\frac{1}{800}\) 2.12 × 10−4 2.01 1.90 × 10−4 2.00 2.34 × 10−5 2.02 7.02 × 10−5 2.01