Using Reproducing Kernel for Solving the Lane-Emden Equations, Arising in Astrophysics

Abstract. In this paper, we utilize an algorithm for solving nonlinear ordinary differential equations of Lane-Emden type on a semi-innite interval. The algorithm is based on an iter- ative technique and the reproducing kernel Hibert method. We give the convergence analysis for the proposed method. The validity and applicability of the proposed method are demon- strated by some numerical examples. The obtained results and comparison with other methods provide conrmation for the validity of our numerical method.