A Nonclassical Radau Collocation Method for Nonlinear Initial-Value Problems with Applications to Lane-Emden Type Equations

Table 4

Comparison of 𝑦(𝑥) for present method, and other methods in the literature for 𝛼=3.

𝑥	Present method	Error	Error in [17]	Error in [15]	Error in [16]	Exact [21]
0.000	1.0000000000	0.00 ×10^0	0.00 ×10^0	0.00 ×10^0	0.00 ×10^0	1.0000000000
0.100	0.9983358295	2.95 ×10^−8	1.82 ×10^−5	1.28 ×10^−5	1.40 ×10^−6	0.9983358000
0.500	0.9598390699	3.00 ×10^−8	1.12 ×10^−4	1.81 ×10^−5	2.99 ×10^−6	0.9598391000
1.000	0.8550575686	3.14 ×10^−8	1.07 ×10^−4	6.00 ×10^−7	1.99 ×10^−6	0.8550576000
5.000	0.1108198351	3.51 ×10^−8	2.02 ×10^−4	2.00 ×10^−7	3.90 ×10^−7	0.1108198000
6.000	0.0437379839	3.90 ×10^−9	5.00 ×10^−5	2.00 ×10^−5	1.14 ×10^−6	0.0437379800
6.800	0.0041677894	4.00 ×10^−10	2.93 ×10^−4	2.79 ×10^−6	1.05 ×10^−5	0.0041677890
6.896	0.0000360111	1.00 ×10^−10	2.10 ×10^−5	1.01 ×10^−6	8.88 ×10^−8	0.0000360112