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

Table 1

Numerical solutions for Example 1.

𝑥	𝑢𝑇(𝑥)	𝑢50	|𝑢𝑇(𝑥)−𝑢50(𝑥)|	|𝑢^′𝑇(𝑥)−𝑢^′50(𝑥)|	|𝑢𝑇^′′(𝑥)−𝑢^′′50(𝑥)|
0.0	1	1	0	0	0.00298864
0.1	0.998337	0.998338	3.37916×10^−7	1.12915×10^−7	3.93668×10^−6
0.2	0.993399	0.9934	3.57116×10^−7	3.49412×10^−7	5.2331×10^−6
0.3	0.985329	0.98533	4.20119×10^−7	9.49753×10^−7	8.31208×10^−6
0.4	0.974355	0.974355	5.53188×10^−7	1.72224×10^−6	1.10979×10^−5
0.5	0.960769	0.96077	7.64858×10^−7	2.49738×10^−6	1.31351×10^−5
0.6	0.944911	0.944912	1.04891×10^−6	3.16098×10^−6	1.37757×10^−5
0.7	0.927146	0.927147	1.39484×10^−6	3.77284×10^−6	1.06634×10^−5
0.8	0.907841	0.907843	1.81934×10^−6	4.9052×10^−6	3.95915×10^−6
0.9	0.887357	0.887359	2.455×10^−6	8.51793×10^−6	5.08462×10^−5
1.0	0.866025	0.866029	3.77266×10^−6	1.98432×10^−5	1.76573×10^−4