The Optimal Homotopy Asymptotic Method for the Solution of Higher-Order Boundary Value Problems in Finite Domains

Table 4

It shows comparison of the OHAM solution (3.18) with the exact solution and the errors obtained by decomposition method (ADM) [19], homotopy perturbation method (HPM) [24], and the variational iteration method [22]. It is clear from the results that the method we applied is more efficient and accurate than the other methods.

𝑥	Exact solution	OHAM sol (3.18)	𝐸^∗ (3.18)	𝐸^∗ (ADM)	𝐸^∗ (HPM)	𝐸^∗ (VIM)
0.0	1	1	0	0	0	0
0.1	0.904837418	0.904837418	−4.82𝐸−10	−1.2𝐸−4	−1.2𝐸−4	−1.2𝐸−4
0.2	0.818730753	0.818730753	−4.92𝐸−10	−2.3𝐸−4	−2.3𝐸−4	−2.3𝐸−4
0.3	0.740818221	0.740818221	−2.37𝐸−11	−3.2𝐸−4	−3.2𝐸−4	−3.2𝐸−4
0.4	0.670320046	0.670320046	5.11𝐸−10	−3.8𝐸−4	−3.8𝐸−4	−3.8𝐸−4
0.5	0.60653066	0.60653066	6.42𝐸−10	−4.0𝐸−4	−4.0𝐸−4	−4.0𝐸−4
0.6	0.548811636	0.548811636	2.02𝐸−10	−3.9𝐸−4	−3.9𝐸−4	−3.9𝐸−4
0.7	0.496585304	0.496585304	−5.37𝐸−10	−3.3𝐸−4	−3.3𝐸−4	−3.3𝐸−4
0.8	0.449328964	0.449328965	−1.02𝐸−09	−2.4𝐸−4	−2.4𝐸−4	−2.4𝐸−4
0.9	0.40656966	0.40656966	−8.23𝐸−10	−1.2𝐸−4	−1.2𝐸−4	−1.2𝐸−4
1.0	0.367879441	0.367879441	−2.05𝐸−12	2.0𝐸−9	2.0𝐸−9	2.0𝐸−9

𝐸^∗ = exact − approximate.