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Table 2 Temporal convergence rates for Example 4.2 with fixed spatial resolution \(J_{x}=400\)

From: Simulation of advection–diffusion–dispersion equations based on a composite time discretization scheme

hσ = 100, ν = 0.1
EAC3AB3
\(E_{\infty }(t)\)\(\mathit{rate}_{t}\)\(E_{R2}(t)\)\(\mathit{rate}_{t}\)cpu\(E_{\infty }(t)\)\(\mathit{rate}_{t}\)\(E_{R2}(t)\)\(\mathit{rate}_{t}\)cpu
2−38.74 × 10−73.71 × 10−40.078.70 × 10−73.71 × 10−40.14
2−41.24 × 10−72.825.26 × 10−52.820.171.23 × 10−72.825.25 × 10−52.820.31
2−51.62 × 10−82.936.91 × 10−62.930.341.61 × 10−82.936.89 × 10−62.930.65
2−62.08 × 10−92.978.84 × 10−72.970.742.06 × 10−92.978.78 × 10−72.971.20
2−72.62 × 10−102.981.12 × 10−72.981.382.64 × 10−102.971.11 × 10−72.992.38
hEAC4AM4
\(E_{\infty }(t)\)\(\mathit{rate}_{t}\)\(E_{R2}(t)\)\(\mathit{rate}_{t}\)cpu\(E_{\infty }(t)\)\(\mathit{rate}_{t}\)\(E_{R2}(t)\)\(\mathit{rate}_{t}\)cpu
2−37.14 × 10−73.03 × 10−40.087.09 × 10−73.03 × 10−40.15
2−41.14 × 10−72.644.87 × 10−52.640.171.14 × 10−72.634.87 × 10−52.640.38
2−51.57 × 10−82.876.67 × 10−62.870.341.61 × 10−82.836.80 × 10−62.840.87
2−62.04 × 10−92.948.69 × 10−72.940.762.33 × 10−92.799.64 × 10−72.821.75
2−72.60 × 10−102.971.11 × 10−72.971.454.72 × 10−102.302.04 × 10−72.243.72