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Table 2 The temporal error and convergence order of the scheme for different γ, α, β with \(\tau^{\min\{3-\gamma,2-\alpha,2-\beta\}}\approx h^{2}\)

From: Finite difference scheme for simulating a generalized two-dimensional multi-term time fractional non-Newtonian fluid model

γ = 1.7, α = 0.8, β = 0.6 \(L_{2} \) error Order \(L_{\infty}\) error Order
τ = 1/20 1.5314E−02   3.0629E−02  
τ = 1/40 6.7733E−03 1.18 1.3138E−02 1.22
τ = 1/80 2.7946E−03 1.28 5.5893E−03 1.23
τ = 1/160 1.2456E−03 1.17 2.4773E−03 1.17
τ = 1/320 5.3792E−04 1.21 1.0758E−03 1.20
γ = 1.5, α = 0.6, β = 0.4 \(L_{2} \) error Order \(L_{\infty}\) error Order
τ = 1/20 8.3425E−03   1.6685E−02  
τ = 1/40 3.1492E−03 1.41 6.2069E−03 1.43
τ = 1/80 1.2085E−03 1.38 2.4035E−03 1.37
τ = 1/160 4.6230E−04 1.39 9.2459E−04 1.38
τ = 1/320 1.7080E−04 1.44 3.4159E−04 1.44
γ = 1.2, α = 0.4, β = 0.2 \(L_{2} \) error Order \(L_{\infty}\) error Order
τ = 1/20 4.3678E−03   8.5587E−03  
τ = 1/40 1.4595E−03 1.58 2.8991E−03 1.56
τ = 1/80 4.8352E−04 1.59 9.6484E−04 1.59
τ = 1/160 1.5651E−04 1.63 3.1303E−04 1.62
τ = 1/320 5.2751E−05 1.57 1.0550E−04 1.57