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

Table 7

Approximation of 𝑦(𝑥) at selected values of 𝑥 using the ADM-SLM approach and the corresponding run times in seconds.

𝑥	[3,1]	[4,1]	[5,1]	[6,1]	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	0.5298369	0.5298364	0.5298364	0.5298364	0.5298364
2.5	0.3747452	0.3747393	0.3747393	0.3747393	0.3747393
3.0	0.2418815	0.2418241	0.2418241	0.2418241	0.2418241
3.5	0.1349246	0.1339693	0.1339690	0.1339690	0.1339690
4.0	0.0745177	0.0488451	0.0488402	0.0488402	0.0488402
Run Time(s)	0.032	0.087	0.891	45.203