Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 10 \(C_{2}\)-order of convergence for Example 1 and different γ’s

From: A new fourth-order explicit group method in the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid

γ = 0.4			γ = 0.5
h/τ	Max error	\(C_{2}\)-order	h/τ	Max error	\(C_{2}\)-order
\(h=\tau =\frac{1}{2}\)	3.7570 × 10⁻²	–	\(h=\tau =\frac{1}{2}\)	4.2072 × 10⁻²	–
\(h=\frac{1}{4}, \tau =\frac{1}{32}\)	2.6621 × 10⁻³	3.81	\(h=\frac{1}{4}, \tau =\frac{1}{32}\)	2.3925 × 10⁻³	4.13
\(h=\tau =\frac{1}{4}\)	1.9645 × 10⁻²	–	\(h=\tau =\frac{1}{4}\)	1.9308 × 10⁻²	–
\(h=\frac{1}{8}, \tau =\frac{1}{64}\)	1.3235 × 10⁻³	3.89	\(h=\frac{1}{8}, \tau =\frac{1}{64}\)	1.2333 × 10⁻³	3.96
γ = 0.6			γ = 0.7
h/τ	Max error	\(C_{2}\)-order	h/τ	Max error	\(C_{2}\)-order
\(h=\tau =\frac{1}{2}\)	4.0658 × 10⁻²	–	\(h=\tau =\frac{1}{2}\)	3.3869 × 10⁻²	–
\(h=\frac{1}{4}, \tau =\frac{1}{32}\)	2.0573 × 10⁻³	4.30	\(h=\frac{1}{4}, \tau =\frac{1}{32}\)	1.6180 × 10⁻³	4.38
\(h=\tau =\frac{1}{4}\)	1.6658 × 10⁻²	–	\(h=\tau =\frac{1}{4}\)	1.2312 × 10⁻²	–
\(h=\frac{1}{8}, \tau =\frac{1}{64}\)	1.0452 × 10⁻³	3.99	\(h=\frac{1}{8}, \tau =\frac{1}{64}\)	8.3252 × 10⁻³	3.88

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