Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 3 \(C_{2}\)-order of convergence for Test problem 1

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

γ = 0.4
h/τ	Max error	\(C_{2}\)-order
\(h =\tau =\frac{1}{2}\)	3.750 × 10⁻²	–
\(h =\frac{1}{4} \), \(\tau =\frac{1}{32}\)	2.612 × 10⁻³	3.84
\(h = \tau =\frac{1}{4}\)	1.966 × 10⁻²	–
\(h =\frac{1}{8} \), \(\tau =\frac{1}{64}\)	1.341 × 10⁻³	3.87

γ = 0.5
h/τ	Max error	\(C_{2}\)-order
\(h =\tau =\frac{1}{2}\)	4.207 × 10⁻²	–
\(h =\frac{1}{4} \), \(\tau =\frac{1}{32}\)	2.390 × 10⁻³	4.13
\(h = \tau =\frac{1}{4}\)	1.931 × 10⁻²	–
\(h =\frac{1}{8} \), \(\tau =\frac{1}{64}\)	1.229 × 10⁻³	3.97

γ = 0.6
h/τ	Max error	\(C_{2}\)-order
\(h = \tau =\frac{1}{2}\)	4.065 × 10⁻²	–
\(h =\frac{1}{4} \), \(\tau =\frac{1}{32}\)	2.047 × 10⁻³	4.31
\(h =\tau =\frac{1}{4}\)	1.665 × 10⁻²	–
\(h =\frac{1}{8} \), \(\tau =\frac{1}{64}\)	1.050 × 10⁻³	3.98

γ = 0.8
h/τ	Max error	\(C_{2}\)-order
\(h =\tau =\frac{1}{2}\)	2.258 × 10⁻²	–
\(h =\frac{1}{4} \), \(\tau =\frac{1}{32}\)	1.105 × 10⁻³	4.35
\(h = \tau =\frac{1}{4}\)	6.946 × 10⁻³	–
\(h =\frac{1}{8} \), \(\tau =\frac{1}{64}\)	4.7880 × 10⁻⁴	3.85

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