A Successive Linearization Method Approach to Solve Lane-Emden Type of Equations

Table 1

Comparison of the first zero (𝛼) of the Lane-Emden equation at different iterations for different values of 𝑛 against numerical results given by Boyd [25] and Seidov [24].

𝑖	𝑛
	𝑛=1	𝑛=2	𝑛=3	𝑛=4
1	3.103790966018498	4.035737655330261	5.557521240863945	8.688676175146224
2	3.141338575299632	4.330814323152805	6.592739714660735	11.771827678456009
3	3.141592635714092	4.352749271550132	6.877461391335034	13.886237798409815
4	3.141592653589793	4.352874592230670	6.896766842576802	14.817460536386396
5	3.141592653589793	4.352874595946125	6.896848617928429	14.967975594173165
6	3.141592653589793	4.352874595946125	6.896848619376960	14.971544376671904
7	3.141592653589793	4.352874595946125	6.896848619376960	14.971546348837493
8	3.141592653589793	4.352874595946125	6.896848619376960	14.971546348838095
Reference [25]	3.141592653589793	4.352874595946125	6.896848619376960	14.971546348838095
Reference [24]	3.141592653589793	4.352874595946124	6.896848619376960	14.971546348838093