A Representation of the Exact Solution of Generalized Lane-Emden Equations Using a New Analytical Method

Table 1

A numerical comparison of the exact error function Ext^𝑘(𝑥) to Example 1 for different values of 𝑥 in [0,10].

𝑥𝑖	Exact solution	Reference [1]	Reference [2]	Present method
0	0	0	0	0
0.01	−0.00000099	6.295572×10^−19	5.790000×10^−8	0
0.1	−0.0009	5.83469×10^−13	8.409000×10^−7	0
0.5	−0.0625	4.937685×10^−9	2.195800×10^−6	0
1	0	1.079378×10^−8	8.284000×10^−7	0
2	8	1.614569×10^−4	1.732000×10^−7	0
5	500	1.80785×10^+2	1.909000×10^−7	0
10	9000	1.894851×10^+6	3.391999×10^−4	0