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

Table 2

Comparison of 𝑦(𝑥) between present method, method in [16] and the exact values for Example 4.1.

𝑥	Method in [16]	Error	Present method	Error	Exact
0.00	0.0000000000	0.00×10^0	0.0000000000	0.00×10^0	0.0000000000
0.01	−0.0001970587	2.93×10^−6	−0.0001999904	4.08×10^−10	−0.0001999900
0.10	−0.0198967225	3.94×10^−6	−0.0199006640	2.27×10^−9	−0.0199006617
0.50	−0.4462840851	3.02×10^−6	−0.4462870994	3.28×10^−9	−0.4462871026
1.00	−1.3862934297	9.31×10^−7	−1.3862943490	1.21×10^−8	−1.3862943611
2.00	−3.2188763248	5.00×10^−7	−3.2188758411	1.63×10^−8	−3.2188758249
3.00	−4.6051709964	8.10×10^−7	−4.6051702055	1.95×10^−8	−4.6051701860
4.00	−5.6664274573	7.69×10^−7	−5.6664266969	8.80×10^−9	−5.6664266881
5.00	−6.5161937402	6.64×10^−7	−6.5161930821	6.09×10^−9	−6.5161930760
6.00	−7.2218363729	5.48×10^−7	−7.2218358310	5.68×10^−9	−7.2218358253
7.00	−7.8240461812	1.70×10^−7	−7.8240460154	4.57×10^−9	−7.8240460109
8.00	−8.3487734467	1.09×10^−7	−8.3487745418	1.97×10^−9	−8.3487745398
9.00	−8.8134506165	1.21×10^−5	−8.8134384925	2.05×10^−9	−8.8134384945
10.00	−9.2302027821	3.83×10^−5	−9.2302410337	1.18×10^−11	−9.2302410337