Skip to main content

Table 4 \(C_{2}\)-order of convergence for Test problem 3

From: High-order compact scheme for the two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid

γ = 0.1
h/τMax error\(C_{2}\)-order
\(h =\tau =\frac{1}{2}\)9.293 × 10−2
\(h =\frac{1}{4} \), \(\tau =\frac{1}{32}\)6.869 × 10−33.76
\(h = \tau =\frac{1}{4}\)4.962 × 10−2
\(h =\frac{1}{8} \), \(\tau =\frac{1}{64}\)3.558 × 10−33.80
γ = 0.2
h/τMax error\(C_{2}\)-order
\(h =\tau =\frac{1}{2}\)8.200 × 10−2
\(h =\frac{1}{4} \), \(\tau =\frac{1}{32}\)5.916 × 10−33.78
\(h = \tau =\frac{1}{4}\)4.298 × 10−2
\(h =\frac{1}{8} \), \(\tau =\frac{1}{64}\)3.058 × 10−33.81
γ = 0.3
h/τMax error\(C_{2}\)-order
\(h =\tau =\frac{1}{2}\)7.092 × 10−2
\(h =\frac{1}{4} \), \(\tau =\frac{1}{32}\)5.068 × 10−33.81
\(h = \tau =\frac{1}{4}\)3.643 × 10−2
\(h =\frac{1}{8} \), \(\tau =\frac{1}{64}\)2.616 × 10−33.80
γ = 0.4
h/τMax error\(C_{2}\)-order
\(h =\tau =\frac{1}{2}\)5.966 × 10−2
\(h =\frac{1}{4} \), \(\tau =\frac{1}{32}\)4.206 × 10−33.83
\(h = \tau =\frac{1}{4}\)2.996 × 10−2
\(h =\frac{1}{8} \), \(\tau =\frac{1}{64}\)2.171 × 10−43.80
γ = 0.5
h/τMax error\(C_{2}\)-order
\(h =\tau =\frac{1}{2}\)4.824 × 10−2
\(h =\frac{1}{4} \), \(\tau =\frac{1}{32}\)3.402 × 10−33.82
\(h = \tau =\frac{1}{4}\)2.359 × 10−2
\(h =\frac{1}{8} \), \(\tau =\frac{1}{64}\)1.669 × 10−33.82
γ = 0.6
h/τMax error\(C_{2}\)-order
\(h =\tau =\frac{1}{2}\)3.668 × 10−2
\(h =\frac{1}{4} \), \(\tau =\frac{1}{32}\)2.652 × 10−33.79
\(h = \tau =\frac{1}{4}\)1.735 × 10−2
\(h =\frac{1}{8} \), \(\tau =\frac{1}{64}\)1.201 × 10−33.85