A Successive Linearization Method Approach to Solve Lane-Emden Type of Equations

Table 3

Comparison of the value of 𝑑𝑦/𝑑𝑡(1), for the Lane-Emden equation at different iterations for different values of 𝑛 against numerical results given by Boyd [25].

𝑖	𝑛
	𝑛=1	𝑛=2	𝑛=3	𝑛=4
1	−1.032146158998257	−0.614886114475695	−0.316160520906889	−0.009814787486055
2	−1.000237675841930	−0.558083545440036	−0.306609857182704	−0.146741321451808
3	−1.000000012692448	−0.553918189951109	−0.293448460329348	−0.128608843668195
4	−1.000000000000000	−0.553897421500438	−0.292634978984266	−0.121103290612396
5	−1.000000000000000	−0.553897420877304	−0.292631615214246	−0.120066832081784
6	−1.000000000000000	−0.553897420877304	−0.292631615154770	−0.120043051612478
7	−1.000000000000000	−0.553897420877304	−0.292631615154770	−0.120043038478707
8	−1.000000000000000	−0.553897420877304	−0.292631615154770	−0.120043038478703
Reference [25]	−1.000000000000000	−0.553897420877304	−0.292631615154770	−0.120043038478703