A Modified Homotopy Perturbation Transform Method for Transient Flow of a Third Grade Fluid in a Channel with Oscillating Motion on the Upper Wall

Table 2

Numerical results show the comparison of new algorithm results with the results obtained from HPM and OHAM for the case of large value of time  𝑡(𝑡=2), when 𝛼=0.5,  𝛽=0.5, 𝜉=−0.5, 𝜔=0.5, 𝐶₁=0.15419514, 𝐶₂=−5.54965331, and 𝐶₂=4.10010429.

𝑧	New method	HPM method	OHAM method	Absolute error	Absolute error
				HPM method	OHAM method
−1	−6.41703×10^−16	2.16947×10^−16	−1.33227×10^−15	8.5865×10^−16	6.550257×10^−16
−0.8	0.1309460	−0.0313209	−0.0275524	0.1622669	0.1584984
−0.6	0.2630750	−0.0593798	−0.0138010	0.3224548	0.2768760
−0.4	0.3968690	−0.0802786	0.0436640	0.4771476	0.3532050
−0.2	0.5312480	−0.0888351	0.1294880	0.6200831	0.4017600
0	0.6623540	−0.0779706	0.2239000	0.7403246	0.4384540
0.2	0.7816650	−0.0383387	0.3090160	0.8200037	0.4726490
0.4	0.8728400	0.041187	0.3730220	0.8316530	0.4998180
0.6	0.9061440	0.170557	0.4152560	0.7355870	0.4908880
0.8	0.8279990	0.349146	0.4542990	0.4788530	0.3737000
1	0.5403020	0.540302	0.5403020	0	0