Table 2 Values of convergence control parameters \( {\overset{\frown }{h}}_f,{\overset{\frown }{h}}_{\theta},\mathrm{and}\;{\overset{\frown }{h}}_{\phi} \) and the corresponding total residual errors \( {E}_m^t \) for different orders of approximation m with S = M = 0.1, Pr = 0.72, γ = 0.1, Nb = Nt = 0.1, Le = 1, A = 0.01, ε 1 = ε 2 = 0.1, θ r  = − 10.0, β = 0.1.
m | \( -{\overset{\frown }{h}}_f \) | \( -{\overset{\frown }{h}}_{\theta} \) | \( -{\overset{\frown }{h}}_{\phi} \) | \( {E}_m^t \) | CPU time (s) |
|---|---|---|---|---|---|
1 | 0.855974 | 0.913900 | 0.213443 | 2.51 × 10−1 | 1.14 |
2 | 0.914521 | 0.894988 | 0.120164 | 1.08 × 10−2 | 5.34 |
3 | 0.905082 | 0.873693 | 0.917802 | 2.98 × 10−4 | 14.92 |
4 | 0.886267 | 0.835341 | 0.896250 | 5.54 × 10−6 | 38.95 |
5 | 0.858155 | 0.913425 | 0.876598 | 2.40 × 10−7 | 72.10 |
6 | 0.821699 | 0.919399 | 0.918880 | 3.42 × 10−8 | 74.52 |