Research Article
New Analytic Solution to the Lane-Emden Equation of Index 2
Table 4
Approximation of at selected values of using the MSLM and the corresponding run times in seconds.
| | 4th order | 6th order | 8th order | 10th order | Numerical [22] |
| 0.5 | 0.9593527 | 0.9593527 | 0.9593527 | 0.9593527 | 0.9593527 | 1.0 | 0.8486544 | 0.8486541 | 0.8486541 | 0.8486541 | 0.8486541 | 1.5 | 0.6953802 | 0.6953672 | 0.6953671 | 0.6953671 | 0.6953671 | 2.0 | 0.5299902 | 0.5298366 | 0.5298364 | 0.5298364 | 0.5298364 | 2.5 | 0.3756041 | 0.3747415 | 0.3747393 | 0.3747393 | 0.3747393 | 3.0 | 0.2448057 | 0.2418367 | 0.2418241 | 0.2418241 | 0.2418241 | 3.5 | 0.1411111 | 0.1340130 | 0.1339691 | 0.1339690 | 0.1339690 | 4.0 | 0.0614816 | 0.0489446 | 0.0488404 | 0.0488402 | 0.0488402 |
| Run Time(s) | 0.031 | 0.047 | 0.328 | 18.610 | |
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