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

Table 1

Approximation of 𝑦(𝑥) for the present method at selected values of 𝑥 using the ADM and the corresponding run times in seconds.

𝑥	10th order	20th order	40th order	60th order	Numerical [22]
0.5	0.9593527	0.9593527	0.9593527	0.9593527	0.9593527
1.0	0.8486541	0.8486541	0.8486541	0.8486541	0.8486541
1.5	0.6953672	0.6953671	0.6953671	0.6953671	0.6953671
2.0	0.5298405	0.5298364	0.5298364	0.5298364	0.5298364
2.5	0.3752294	0.3747394	0.3747393	0.3747393	0.3747393
3.0	0.2657006	0.2419943	0.2418241	0.2418241	0.2418241
3.5	0.7567158	0.2311776	0.1352586	0.1339821	0.1339690
4.0	10.3508034	23.34921747	64.6821008	137.0780406	0.0488402
Run time	0.016	0.016	0.110	0.375