Solution of the Lane-Emden Equation Using the Bernstein Operational Matrix of Integration

Table 1

Comparison of the numerical solution and error obtained by present method for 𝑛=3 in (36) with series solution [25].

𝑥	Our method			Series method [25]
	𝑚=32	𝑚=128	𝑚=256
0.0	0.00𝐸+00	0.00𝐸+00	0.00𝐸+00	0.00𝐸+00
0.1	4.02𝐸−05	2.51𝐸−06	6.28𝐸−07	1.40𝐸−06
0.5	2.89𝐸−05	1.85𝐸−06	4.96𝐸−07	2.99𝐸−06
1.0	4.39𝐸−05	3.79𝐸−05	3.76𝐸−05	1.99𝐸−06