Bernstein Series Solution of a Class of Lane-Emden Type Equations

Table 5

Comparison of 𝑦(𝑥), between present method and HFC method for Example 10, digits: 50.

𝑡	Bernstein series solutions		Corrected Bernstein series solution	HFC method [18]
	𝑛=10	𝑛=20	𝑛=10, 𝑚=12	𝑛=30, 𝑘=6, 𝑙=2
0.00	0.00	0.00	0.00	0.00
0.01	4.05𝐸−9	4.77𝐸−17	4.29𝐸−14	2.24𝐸−8
0.02	1.39𝐸−8	1.33𝐸−16	5.88𝐸−13	1.58𝐸−8
0.05	5.47𝐸−8	3.16𝐸−16	1.80𝐸−12	2.12𝐸−8
0.10	1.03𝐸−7	3.90𝐸−16	8.45𝐸−12	1.78𝐸−8
0.20	1.26𝐸−7	4.34𝐸−16	1.88𝐸−11	2.09𝐸−8
0.50	1.67𝐸−7	5.57𝐸−16	4.36𝐸−11	2.62𝐸−8
0.70	2.14𝐸−7	7.11𝐸−16	1.00𝐸−10	3.27𝐸−8
0.80	2.52𝐸−7	8.27𝐸−16	2.17𝐸−10	3.79𝐸−6
0.90	1.65𝐸−7	9.87𝐸−16	2.53𝐸−10	5.48𝐸−8
1.00	5.90𝐸−6	2.75𝐸−14	7.52𝐸−8	2.51𝐸−9