Variational Iteration Method for Fifth-Order Boundary Value Problems Using He's Polynomials

Table 2

Error estimates.

𝑥	Exact solution	^*Errors
		HPM	B-spline	VIM	ADM	ITM	VIMHP
0.0	0.000000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
0.1	0.099465	–3E–11	–8.0E–3	–3E–11	–3E–11	–3E–11	–3E–11
0.2	0.195424	–2E–10	–1.2 E–3	–2E–10	–2E–10	–2E–10	–2E–10
0.3	0.283470	–4E–10	–5.0 E–3	–4E–10	–4E–10	–4E–10	–4E–10
0.4	0.358038	–8E–10	3.0 E–3	–8E–10	–8E–10	–8E–10	–8E–10
0.5	0.412180	–1.2E–9	8.0 E–3	–1.2E–9	–1.2E–9	–1.2E–9	–1.2E–9
0.6	0.437309	–2E–9	6.0 E–3	–2E–9	–2E–9	–2E–9	–2E–9
0.7	0.422888	–2.2E–9	–0.000	–2.2E–9	–2.2E–9	–2.2E–9	–2.2E–9
0.8	0.356087	–1.9E–9	9.0 E–3	–1.9E–9	–1.9E–9	–1.9E–9	–1.9E–9
0.9	0.221364	–1.4E–9	–9.0E–3	–1.4E–9	–1.4E–9	–1.4E–9	–1.4E–9
1.0	0.000000	0.000	0.000000	0.000	0.000	0.000	0.000

^*Error = exact solution − series solution.