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

Table 1

The ∞-norms of the absolute errors, estimations of the absolute errors, the ∞-norms of the corrected absolute errors, and upper bounds of the absolute errors for Example 9.

𝑛	‖𝑓−𝑝𝑛‖∞	‖𝑒^∗12‖∞	‖𝑓−𝑝𝑛−𝑒^∗12‖∞	Expected upper bound by using Theorem 4
3	0.0035	0.0035	0.47𝐸−10	0.0771
4	0.00028	0.00028	0.47𝐸−10	0.0193
5	0.6543𝐸−4	0.6543𝐸−4	0.4710𝐸−10	0.0059
6	0.7244𝐸−5	0.7244𝐸−5	0.4710𝐸−10	0.0018
7	0.1422𝐸−5	0.1422𝐸−5	0.4710𝐸−10	6.0181𝐸−4
8	0.1808𝐸−6	0.1807𝐸−6	0.4710𝐸−10	2.3542𝐸−4
9	0.3298𝐸−7	0.3293𝐸−7	0.4710𝐸−10	9.5485𝐸−5
10	0.4496𝐸−8	0.4451𝐸−8	0.4710𝐸−10	4.0126𝐸−5
11	0.7905𝐸−9	0.7445𝐸−9	0.4710𝐸−10	1.6817𝐸−5
12	0.1119𝐸−9	0.6644𝐸−10	0.4710𝐸−10	0.8036𝐸−5
13	0.1930𝐸−10	0.1757𝐸−10	0.1745𝐸−11	0.3764𝐸−5
14	0.2796𝐸−11	0.2365𝐸−12	0.2772𝐸−11	0.1757𝐸−5
15	0.5043𝐸−12	0.4189𝐸−12	0.8734𝐸−13	0.8044𝐸−6
16	0.3273𝐸−13	0.5776𝐸−13	0.2526𝐸−13	0.4066𝐸−6
17	0.1046𝐸−11	0.7751𝐸−12	0.1712𝐸−11	0.2010𝐸−6