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Theory and Modern Applications

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