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

Table 1

It shows comparison of the solutions obtained by OHAM (3.7), ADM [18], HPM [20], VIM [22], ITM [24], and VIHPM [21]. From the numerical results, it is clear that OHAM is more efficient and accurate.

𝑥	Exact sol.	OHAM sol.	𝐸^∗ (3.7)	𝐸^∗ (ADM)	𝐸^∗ (HPM)	𝐸^∗ (VIM)	𝐸^∗ (ITM)	𝐸^∗ (VIHPM)
0.0	0.00000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
0.1	0.099465383	0.099465383	−1𝐸−12	−3𝐸−11	−3𝐸−11	−3𝐸−11	−3𝐸−11	−3𝐸−11
0.2	0.195424441	0.195424441	−7𝐸−12	−2𝐸−10	−2𝐸−10	−2𝐸−10	−2𝐸−10	−2𝐸−10
0.3	0.28347035	0.28347035	−1𝐸−11	−4𝐸−10	−4𝐸−10	−4𝐸−10	−4𝐸−10	−4𝐸−10
0.4	0.358037927	0.358037927	−1𝐸−11	−8𝐸−10	−8𝐸−10	−8𝐸−10	−8𝐸−10	−8𝐸−10
0.5	0.412180318	0.412180318	−8𝐸−12	−1𝐸−9	−1𝐸−9	−1𝐸−9	−1𝐸−9	−1𝐸−9
0.6	0.437308512	0.437308512	3𝐸−14	−2𝐸−9	−2𝐸−9	−2𝐸−9	−2𝐸−9	−2𝐸−9
0.7	0.422888068	0.422888068	6𝐸−12	−2𝐸−9	−2𝐸−9	−2𝐸−9	−2𝐸−9	−2𝐸−9
0.8	0.356086548	0.356086548	2𝐸−12	−2𝐸−9	−2𝐸−9	−2𝐸−9	−2𝐸−9	−2𝐸−9
0.9	0.221364280	0.221364280	−3𝐸−11	−1𝐸−9	−1𝐸−9	−1𝐸−9	−1𝐸−9	−1𝐸−9
1.0	0.0000	0.000	0.000	0.000	0.000	0.000	0.000	0.000

𝐸^∗ = exact – approximate.