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-infinite interval‎. ‎The algorithm is based on an iterative technique and the‎reproducing kernel Hibert method‎. ‎We give‎ the convergence analysis for the proposed method‎. ‎The validity and applicability of the proposed‎ ‎method are demonstrated by some numerical examples‎. ‎The obtained results and comparison with‎ ‎other methods provide confirmation for the validity of our numerical method‎.