On using a modified Legendre-spectral method for solving singular IVPs of Lane–Emden type

In this paper, approximate solutions of singular initial value problems (IVPs) of the Lane–Emden type in second-order ordinary differential equations (ODEs) are obtained by an improved Legendre-spectral method. The Legendre–Gauss points are used as collocation nodes and Lagrange interpolation is employed in the Volterra term. The results reveal that the method is effective, simple and accurate.