orthogonal collocation

A hybrid computational procedure of Newton Raphson method and orthogonal collocation method have been applied to study the behavior of nonlinear astrophysics equations. The nonlinear Lane Emden equation has been discretized using the orthogonal collocation method using $n^{th}$-order Bessel polynomial as $J_n(\xi)$ as base function.  The system of collocation equations has been solved numerically using Newton Raphson method. Numerical examples have been discussed to check the reliability and efficiency of the scheme. Numerically calculated results have been compared to the exact values as well as the values already given in the literature to check the compatibility of the scheme. Error analysis has been studied by calculating the absolute error, $L_2- norm$ and $L_{\infty}- norm$. Computer codes have been prepared using MATLAB.