Rational Homotopy Perturbation Method

Table 1

Comparison of the relative error between exact solution (4.2) for (4.1) to the results of approximations (4.11), (4.14), (4.19), and (4.22).

		Homotopy (4.3)	Homotopy (4.3)	Homotopy (4.4)	Homotopy (4.4)
Order		[3,2]	10	[2,1]	2
𝑥	Exact (4.2)	RHPM (4.11)	HPM (4.19)	RHPM (4.14)	HPM (4.22)
0.50	−0.462117	2.82139e − 13	−9.2001e − 12	0.0131193	0.00872875
1.00	−0.761594	7.99295e − 10	−3.6699e − 05	0.0127018	−0.0076966
1.50	−0.905148	6.27205e − 08	−0.254724	0.00372419	−0.0365396
2.00	−0.964028	1.12495e − 06	−130.396	−0.00187676	−0.0563138
2.50	−0.986614	9.09157e − 06	−16013.2	−0.0030716	−0.061996
3.00	−0.995055	4.49154e − 05	−799594	−0.00226142	−0.0574954
3.50	−0.998178	0.000159567	−2.152e + 07	−0.00114353	−0.0481177
4.00	−0.999329	0.000448827	−3.695e + 08	−0.000334271	−0.0376627
4.50	−0.999753	0.00106284	−4.508e + 09	0.000105112	−0.0281496
5.00	−0.999909	0.0022083	−4.206e + 10	0.000282807	−0.0203519
8.00	−1.000000	0.0372487	−8.607e + 14	8.27086e − 05	−0.00201311
100	−1.000000	358.626	−9.689e + 37	3.43629e − 44	−3.64567e − 42