A General Solution for Troesch's Problem

Table 2

Comparison between (3.14), exact solution [8, 9], and other reported approximate solutions, using 𝑛=1.

𝑥	Exact [8]	This work (3.14)	ADM [13]	HPM [12]	HPM [11]	HAM [14]	LDTM [16]
0.1	0.0846612565	0.08466075858	0.084248760	0.0843817004	0.084934415	0.0846732692	0.08466308972
0.2	0.1701713582	0.1701704581	0.169430700	0.1696207644	0.170697546	0.1701954538	0.1701750442
0.3	0.2573939080	0.2573927827	0.256414500	0.2565929224	0.258133224	0.2574302342	0.2573994845
0.4	0.3472228551	0.3472217324	0.346085720	0.3462107378	0.348116627	0.3472715981	0.3472303763
0.5	0.4405998351	0.4405989511	0.439401985	0.4394422743	0.44157274	0.4406610140	0.4406093753
0.6	0.5385343980	0.5385339413	0.537365700	0.5373300622	0.539498234	0.5386072529	0.5385460046
0.7	0.6421286091	0.6421286573	0.641083800	0.6410104651	0.642987984	0.7526899495	0.6421421393
0.8	0.7526080939	0.7526085475	0.751788000	0.7517335467	0.753267551	0.7526899495	0.7526226886
0.9	0.8713625196	0.8713630450	0.870908700	0.8708835371	0.871733059	0.8714249118	0.8713748860
	Order	2	6	2	2	6	3
	A.A.R.E.	2.54568𝑒(−06)	0.002714577	0.002320107	0.002044737	0.019244326	2.05𝑒(−05)