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Table 2 Spatial convergence rate for Example 2 with fixed \(h=0.00002\)

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

\(M_{x}=M_{y}\) 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
20 7.45 × 10−6 7.81 × 10−6 2.11 × 10−5 1.30 × 10−5
40 1.36 × 10−7 5.78 3.28 × 10−7 4.58 1.31 × 10−6 4.02 8.67 × 10−7 3.90
80 1.33 × 10−8 3.36 2.47 × 10−8 3.73 8.16 × 10−8 4.00 5.51 × 10−8 3.98
160 9.59 × 10−10 3.79 1.64 × 10−9 3.91 5.24 × 10−9 3.96 3.58 × 10−9 3.94
320 9.00 × 10−11 3.41 1.67 × 10−10 3.30 5.05 × 10−10 3.38 3.60 × 10−10 3.31
ν = 0.01
40 4.04 × 10−2 2.16 × 10−2 2.63 × 10−2 3.13 × 10−3
80 5.90 × 10−4 6.10 3.84 × 10−4 5.81 8.02 × 10−4 5.03 2.07 × 10−4 3.92
160 5.06 × 10−5 3.54 3.00 × 10−5 3.68 5.51 × 10−5 3.86 1.35 × 10−5 3.94
320 3.18 × 10−6 3.99 2.08 × 10−6 3.85 3.39 × 10−6 4.02 8.58 × 10−7 3.98
640 1.98 × 10−7 4.01 1.33 × 10−7 3.96 2.28 × 10−7 3.90 5.99 × 10−8 3.84