Research Article
Using an Effective Numerical Method for Solving a Class of Lane-Emden Equations
Table 3
Numerical solutions for Example
3.
| | Exact solution | 50-order RKM approximation | 100-order RKM approximation | 150-order RKM approximation | | | | |
| 0.0 | 0 | 0 | 0 | 0 | 0.1 | 0.009 | 0.00886466 | 0.00897728 | 0.00899228 | 0.2 | 0.032 | 0.0318207 | 0.0319718 | 0.0319906 | 0.3 | 0.063 | 0.0627957 | 0.0629686 | 0.0629896 | 0.4 | 0.096 | 0.0957782 | 0.0959661 | 0.0959888 | 0.5 | 0.125 | 0.124764 | 0.124964 | 0.124988 | 0.6 | 0.144 | 0.143752 | 0.143962 | 0.143987 | 0.7 | 0.147 | 0.146741 | 0.14696 | 0.146986 | 0.8 | 0.128 | 0.12773 | 0.127957 | 0.127985 | 0.9 | 0.081 | 0.0807176 | 0.0809539 | 0.0809837 | 1.0 | 0 | −0.000295352 | −0.0000496372 | −0.0000179019 |
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