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