Numerical Solution of Singular Lane-Emden Equation

Table 1

Numerical results of Example 1.

𝑥	Exact solution	Legendre wavelets	Absolute error
0.0	1	1.000020858	0.000020858
0.1	0.9900498337	0.9900449375	0.0000048962
0.2	0.9607894392	0.9607962885	0.0000068493
0.3	0.9139311853	0.9139303816	8.037×10^−7
0.4	0.8521437890	0.8521354021	0.0000083869
0.5	0.7788007831	0.7787879122	0.0000128709
0.6	0.6976763261	0.6976230812	0.0000532449
0.7	0.6126263942	0.6124194854	0.0002069088
0.8	0.5272924240	0.5266984761	0.0005939479
0.9	0.4448580662	0.4434381168	0.0014199494
1	0.3678794412	0.3648016892	0.0030777520