Using an Effective Numerical Method for Solving a Class of Lane-Emden Equations

Table 5

Numerical solutions for Example 5.

𝑥	Exact solution	50-order RKM approximation	The approximation solutions in [3]
	𝑢𝑇(𝑥)	𝑢50(𝑥)	𝑢(𝑥) in [3]
0.0	0	0	0
0.01	−0.0001999900	−0.00019999	−0.0001970587
0.1	−0.0199006617	−0.0199007	−0.0198967225
0.5	−0.4462871026	−0.446287	−0.4462840851
1.0	−1.3862943611	−1.38629	−1.3862934297
2.0	−3.2188758249	−3.21888	−3.2188763248
3.0	−4.6051701860	−4.60517	−4.6051709964
4.0	−5.6664266881	−5.66643	−5.6664274573