Rational Homotopy Perturbation Method

Table 2

Comparison of the relative error between exact solution (5.2) for (5.1) and its first order approximate solutions given by RHPM (5.7), HPM [3], and VIM [3].

Order		[1,1]	1	1
𝑡	Exact (4.2)	RHPM (5.7)	HPM [3]	VIM [3]
0.5	0.47942554	0.00219553	0.00007743	0.00080698
1.0	0.84147098	0.00629261	0.00389778	0.02403725
1.5	0.99749499	0.00924481	0.03354518	0.17347474
2.0	0.90929743	0.01132241	0.14119662	0.74571902
2.5	0.59847214	0.00061706	0.44219762	2.85423607
3.0	0.14112001	−0.06022780	2.40024981	23.28655437