A numerical method for solving the Lane-Emden equations of the polytropic index a when 4:75 6 a 6 5 is
introduced. The method is based upon nonclassical Gauss-Radau collocation points and Freud type weights. Nonclassical
orthogonal polynomials, nonclassical Radau points and weighted interpolation are introduced and are utilized in the interval
[0;1]. A smooth, strictly monotonic transformation is used to map the infinite domain x 2 [0;¥) onto a half-open interval
t 2 [0;1). The resulting problem on the finite interval is then transcribed to a system of nonlinear algebraic equations using
collocation. The method is easy to implement and yields very accurate results.
