The Numerical Method for Solving Differential Equations of Lane-Emden Type by Padé Approximation

Table 2

Numerical solution of 𝑢(𝑥).

𝑥	𝑢(𝑥)	𝑃[5/4]	|𝑢(𝑥)−𝑃[5/4]|
0.1	1.010050167	1.010050167	0
0.2	1.040810774	1.040810774	0
0.3	1.094174234	1.094174275	4.1×10^−8
0.4	1.173509974	1.173510700	7.26×10^−7
0.5	1.284016927	1.284023668	0.000006741
0.6	1.433275840	1.43317285	0.000041445
0.7	1.632060167	1.632251266	0.000191099
0.8	1.895481174	1.896191187	0.000710013
0.9	2.244559634	2.246777235	0.002217601
1.0	2.708333334	2.714285714	0.005952380