Numerical solution of singular IVPs of Lane–Emden type using a modified Legendre-spectral method

In this paper, a numerical method for singular initial value problems of the Lane–Emden type in the second-order ordinary differential equations is proposed. The method changes solving the equation to solving a Volterra integral equation. We have applied the improved Legendre-spectral method to solve Lane–Emden type equations. The Legendre Gauss points are used as collocation nodes and Lagrange interpolation is employed in Volterra term. The results reveal that the method is effective, simple and accurate.