Abstract
If the set of basis functions is chosen by overlooking physics of a problem, then the results can be misleading. It is shown that for the Lane-Emden equation, a set of functions with semi-infinite domain sometimes fails to produce results of desired accuracy. A qualitative analysis of the problem shows that the solution is bounded when m is an odd integer but is unbounded when m is even. Solution of the Lane-Emden equation with rational Legendre functions, as basis, is poorer in accuracy when m = 2 as compared with the one when m = 3 with the same basis. Since the physically important region is contained in a finite interval, a set of scaled Legendre polynomials, as basis, produces results which are much more accurate on the interval of interest.