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 2 Comparison between Crank–Nicolson (C–N) high-order finite difference method and HEGM for Example 2 when \(\gamma =0.5\)

h/τ	Iteration		Time		Maximum error		Average error
h/τ	HEGM	C–N	HEGM	C–N	HEGM	C–N	HEGM	C–N
\(h=\tau =\frac{1}{10}\)	46	50	16.22	18.37	7.5870 ×10⁻³	7.5733 ×10⁻³	4.3269 ×10⁻³	4.3301 ×10⁻³
\(h=\tau =\frac{1}{18}\)	48	52	207.69	224.26	4.3170 ×10⁻³	4.3041 ×10⁻³	2.2571 ×10⁻³	2.2547 ×10⁻³
\(h=\tau =\frac{1}{22}\)	47	57	483.15	594.33	3.5419 ×10⁻³	3.5520 ×10⁻³	1.8133 ×10⁻³	1.8190 ×10⁻³
\(h=\tau =\frac{1}{30}\)	47	65	2018.26	2727.72	2.6249 ×10⁻³	2.6329 ×10⁻³	1.3123 ×10⁻³	1.3130 ×10⁻³