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 1

Numerical results show the comparison of new algorithm results with the results obtained from HPM and OHAM for the case of small value of time  𝑡(𝑡=0.1), 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 algorithm	HPM method	OHAM method	Absolute error	Absolute error
				HPM method	OHAM method
−1	−1.43639×10^−16	3.03836×10^−17	4.44089×10^−16	2.89467×10^−17	5.87728×10^−16
−0.8	0.0401522	0.0269116	0.0315324	0.0132406	0.0086198
−0.6	0.0829870	0.0565498	0.0698092	0.0264372	0.0131778
−0.4	0.1313580	0.0919104	0.1180830	0.0394476	0.0132750
−0.2	0.1884740	0.1365570	0.1783360	0.051917	0.0101380
0	0.2580990	0.1949830	0.2527330	0.063116	0.0053660
0.2	0.3447890	0.2730870	0.3443530	0.071702	0.0004360
0.4	0.4541750	0.3788420	0.4576250	0.075333	0.0034500
0.6	0.5933060	0.5232930	0.5986640	0.070013	0.0053580
0.8	0.7710760	0.7221790	0.7755630	0.048897	0.0044870
1	0.9987500	0.998750	0.998750	0	0