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Theory and Modern Applications

Table 1 Comparison between Crank–Nicolson (C–N) high-order finite difference method and HEGM for Example 1 when \(\gamma =0.75\)

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

h/τ

Iteration

Time

Maximum error

Average error

HEGM

C–N

HEGM

C–N

HEGM

C–N

HEGM

C–N

\(h=\tau =\frac{1}{10}\)

46

53

16.59

19.23

3.9320 ×10−3

3.9473 ×10−3

2.2799 ×10−3

2.2815 ×10−3

\(h=\tau =\frac{1}{18}\)

49

52

208.44

220.02

2.4058 ×10−3

2.4059 ×10−3

1.2545 ×10−3

1.2567 ×10−3

\(h=\tau =\frac{1}{22}\)

48

57

514.81

603.56

2.0054 ×10−3

2.0087 ×10−3

1.0222 ×10−3

1.0258 ×10−3

\(h=\tau =\frac{1}{30}\)

47

65

1902.32

2571.45

1.5041 ×10−3

1.5053 ×10−3

7.4966 ×10−4

7.5067 ×10−4