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

Table 5

𝑥	Exact	OHAM sol.	𝐸^∗ (3.22)	𝐸^∗ (3.24)	𝐸^∗ (3.26)	𝐸^∗ ([25])
0.0	1	1	0	0	0	0
0.1	1.105170918	1.105170915	2.60𝐸−9	−3.5𝐸−12	1.39𝐸−16	1.27𝐸−5
0.2	1.221402758	1.221402732	2.62𝐸−8	−3.5𝐸−11	5.32𝐸−16	2.43𝐸−5
0.3	1.349858808	1.349858729	7.86𝐸−8	−1.1𝐸−10	1.48𝐸−15	3.35𝐸−5
0.4	1.491824698	1.491824562	1.36𝐸−7	−1.8𝐸−10	3.36𝐸−15	3.94𝐸−5
0.5	1.648721271	1.648721109	1.61𝐸−7	−2.2𝐸−10	2.28𝐸−14	4.16𝐸−5
0.6	1.822118800	1.822118662	1.39𝐸−7	−1.9𝐸−10	2.21𝐸−13	3.96𝐸−5
0.7	2.013752707	2.013752625	8.22𝐸−8	−1.1𝐸−10	1.64𝐸−12	3.38𝐸−5
0.8	2.225540928	2.225540900	2.80𝐸−8	−2.8𝐸−11	9.36𝐸−12	2.45𝐸−5
0.9	2.459603111	2.459603108	2.84𝐸−9	4.1𝐸−11	4.36𝐸−11	1.29𝐸−5
1.0	2.718281828	2.718281828	1.14𝐸−13	1.8𝐸−10	1.73𝐸−10	1.00𝐸−9

𝐸^∗ = exact − approximate.