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

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 5 Comparison between C–N high-order finite difference method and HEGM for Example 3 when \(\gamma =0.75\)

h/τ	Iteration		Time		Maximum error		Average error
h/τ	HEGM	C–N	HEGM	C–N	HEGM	C–N	HEGM	C–N
\(h=\tau =\frac{1}{10}\)	44	48	46.75	53.44	1.1762 ×10⁻²	1.1780 ×10⁻²	2.0762 ×10⁻³	2.0850 ×10⁻³
\(h=\tau =\frac{1}{14}\)	44	52	152.45	188.46	8.5326 ×10⁻³	8.7058 ×10⁻⁴	9.1589 ×10⁻⁴	9.1579 ×10⁻⁴
\(h=\tau =\frac{1}{18}\)	45	58	462.44	552.32	4.9486 ×10⁻³	4.9496 ×10⁻³	5.9148 ×10⁻⁴	5.9035 ×10⁻⁴
\(h=\tau =\frac{1}{22}\)	48	56	828.46	1158.37	1.8846 ×10⁻³	1.8875 ×10⁻⁴	2.6648 ×10⁻⁴	2.6678 ×10⁻⁴