New Analytic Solution to the Lane-Emden Equation of Index 2

Table 2

Errors of the ADM method at selected values of 𝑥.

𝑥	10th order	20th order	40th order	60th order
0.5	0.0000000	0.0000000	0.0000000	0.0000000
1.0	0.0000000	0.0000000	0.0000000	0.0000000
1.5	0.0000001	0.0000000	0.0000000	0.0000000
2.0	0.0000041	0.0000000	0.0000000	0.0000000
2.5	0.0004901	0.0000001	0.0000000	0.0000000
3.0	0.0238765	0.0001702	0.0000000	0.0000000
3.5	0.6227468	0.0972086	0.0012896	0.0000131
4.0	10.3019632	23.3003773	64.6332606	137.0292005