Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 11 \(C_{2}\)-order of convergence of HEGM for Example 2 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
\(h=\tau =\frac{1}{2}\)	1.1717	–	\(h=\tau =\frac{1}{2}\)	1.1891	–
\(h=\frac{1}{4}, \tau =\frac{1}{32}\)	6.8679 × 10⁻²	4.09	\(h=\frac{1}{4}, \tau =\frac{1}{32}\)	6.8093 × 10⁻²	4.12
\(h=\tau =\frac{1}{4}\)	8.5608 × 10⁻²	–	\(h=\tau =\frac{1}{4}\)	8.7109 × 10⁻²	–
\(h=\frac{1}{8}, \tau =\frac{1}{64}\)	5.1955 × 10⁻³	4.04	\(h=\frac{1}{8}, \tau =\frac{1}{64}\)	4.8825 × 10⁻³	4.15
γ = 0.6			γ = 0.7
h/τ	Max error	\(C_{2}\)-order	h/τ	Max error	\(C_{2}\)-order
\(h=\tau =\frac{1}{2}\)	1.1802	–	\(h=\tau =\frac{1}{2}\)	1.1474	–
\(h=\frac{1}{4}, \tau =\frac{1}{32}\)	6.7241 × 10⁻²	4.13	\(h=\frac{1}{4}, \tau =\frac{1}{32}\)	6.6197 × 10⁻²	4.11
\(h=\tau =\frac{1}{4}\)	8.2701 × 10⁻²	–	\(h=\tau =\frac{1}{4}\)	7.3781 × 10⁻²	–
\(h=\frac{1}{8}, \tau =\frac{1}{64}\)	4.4968 × 10⁻³	4.20	\(h=\frac{1}{8}, \tau =\frac{1}{64}\)	4.0021 × 10⁻³	4.20

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